Hilbert curve: Difference between revisions
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m (→{{header|Sidef}}: updated code: use round() instead of int()) |
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y = (n - 1) - y; |
y = (n - 1) - y; |
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} |
} |
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std::swap(x, y); |
std::swap(x, y); |
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} |
} |
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} |
} |
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int calcD(int n) { |
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bool rx, ry; |
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int d = 0; |
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for (int s = n >> 1; s > 0; s >>= 1) { |
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rx = ((x & s) != 0); |
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ry = ((y & s) != 0); |
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d += s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0)); |
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rot(s, rx, ry); |
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} |
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return d; |
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} |
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friend std::ostream &operator<<(std::ostream &, const Point &); |
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}; |
}; |
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std::ostream &operator<<(std::ostream &out, const Point &p) { |
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return out << '(' << p.x << ", " << p.y << ')'; |
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} |
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Point fromD(int n, int d) { |
Point fromD(int n, int d) { |
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| Line 290: | Line 271: | ||
std::cout << '\n'; |
std::cout << '\n'; |
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} |
} |
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return 0; |
return 0; |
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}</lang> |
}</lang> |
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Revision as of 21:37, 3 March 2020
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Produce a graphical or ASCII-art representation of a Hilbert curve of at least order 3.
ALGOL 68
This generates the curve following the L-System rules described in the Wikipedia article.
| L-System rule | A | B | F | + | - |
| Procedure | a | b | forward | right | left |
<lang algol68>BEGIN
INT level = 4; # <-- change this #
INT side = 2**level * 2 - 2; [-side:1, 0:side]STRING grid; INT x := 0, y := 0, dir := 0; INT old dir := -1; INT e=0, n=1, w=2, s=3;
FOR i FROM 1 LWB grid TO 1 UPB grid DO FOR j FROM 2 LWB grid TO 2 UPB grid DO grid[i,j] := " " OD OD;
PROC left = VOID: dir := (dir + 1) MOD 4;
PROC right = VOID: dir := (dir - 1) MOD 4;
PROC move = VOID: (
CASE dir + 1 IN
# e: # x +:= 1, # n: # y -:= 1, # w: # x -:= 1, # s: # y +:= 1
ESAC
);
PROC forward = VOID: (
# draw corner #
grid[y, x] := CASE old dir + 1 IN
# e # CASE dir + 1 IN "──", "─╯", " ?", "─╮" ESAC,
# n # CASE dir + 1 IN " ╭", " │", "─╮", " ?" ESAC,
# w # CASE dir + 1 IN " ?", " ╰", "──", " ╭" ESAC,
# s # CASE dir + 1 IN " ╰", " ?", "─╯", " │" ESAC
OUT " "
ESAC;
move;
# draw segment #
grid[y, x] := IF dir = n OR dir = s THEN " │" ELSE "──" FI;
# advance to next corner #
move;
old dir := dir
);
PROC a = (INT level)VOID:
IF level > 0 THEN
left; b(level-1); forward; right; a(level-1); forward;
a(level-1); right; forward; b(level-1); left
FI,
b = (INT level)VOID:
IF level > 0 THEN
right; a(level-1); forward; left; b(level-1); forward;
b(level-1); left; forward; a(level-1); right
FI;
# draw # a(level);
# print # FOR row FROM 1 LWB grid TO 1 UPB grid DO print((grid[row,], new line)) OD
END </lang>
- Output:
╭───╮ ╭───╮ ╭───╮ ╭───╮ ╭───╮ ╭───╮ ╭───╮ ╭───╮
│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
│ ╰───╯ │ │ ╰───╯ │ │ ╰───╯ │ │ ╰───╯ │
│ │ │ │ │ │ │ │
╰───╮ ╭───╯ ╰───╮ ╭───╯ ╰───╮ ╭───╯ ╰───╮ ╭───╯
│ │ │ │ │ │ │ │
╭───╯ ╰───────────╯ ╰───╮ ╭───╯ ╰───────────╯ ╰───╮
│ │ │ │
│ ╭───────╮ ╭───────╮ │ │ ╭───────╮ ╭───────╮ │
│ │ │ │ │ │ │ │ │ │ │ │
╰───╯ ╭───╯ ╰───╮ ╰───╯ ╰───╯ ╭───╯ ╰───╮ ╰───╯
│ │ │ │
╭───╮ ╰───╮ ╭───╯ ╭───╮ ╭───╮ ╰───╮ ╭───╯ ╭───╮
│ │ │ │ │ │ │ │ │ │ │ │
│ ╰───────╯ ╰───────╯ ╰───╯ ╰───────╯ ╰───────╯ │
│ │
╰───╮ ╭───────╮ ╭───────╮ ╭───────╮ ╭───────╮ ╭───╯
│ │ │ │ │ │ │ │ │ │
╭───╯ ╰───╮ ╰───╯ ╭───╯ ╰───╮ ╰───╯ ╭───╯ ╰───╮
│ │ │ │ │ │
│ ╭───╮ │ ╭───╮ ╰───╮ ╭───╯ ╭───╮ │ ╭───╮ │
│ │ │ │ │ │ │ │ │ │ │ │ │ │
╰───╯ ╰───╯ │ ╰───────╯ ╰───────╯ │ ╰───╯ ╰───╯
│ │
╭───╮ ╭───╮ │ ╭───────╮ ╭───────╮ │ ╭───╮ ╭───╮
│ │ │ │ │ │ │ │ │ │ │ │ │ │
│ ╰───╯ │ ╰───╯ ╭───╯ ╰───╮ ╰───╯ │ ╰───╯ │
│ │ │ │ │ │
╰───╮ ╭───╯ ╭───╮ ╰───╮ ╭───╯ ╭───╮ ╰───╮ ╭───╯
│ │ │ │ │ │ │ │ │ │
───╯ ╰───────╯ ╰───────╯ ╰───────╯ ╰───────╯ ╰──
C
<lang c>#include <stdio.h>
- define N 32
- define K 3
- define MAX N * K
typedef struct { int x; int y; } point;
void rot(int n, point *p, int rx, int ry) {
int t;
if (!ry) {
if (rx == 1) {
p->x = n - 1 - p->x;
p->y = n - 1 - p->y;
}
t = p->x;
p->x = p->y;
p->y = t;
}
}
void d2pt(int n, int d, point *p) {
int s = 1, t = d, rx, ry;
p->x = 0;
p->y = 0;
while (s < n) {
rx = 1 & (t / 2);
ry = 1 & (t ^ rx);
rot(s, p, rx, ry);
p->x += s * rx;
p->y += s * ry;
t /= 4;
s *= 2;
}
}
int main() {
int d, x, y, cx, cy, px, py;
char pts[MAX][MAX];
point curr, prev;
for (x = 0; x < MAX; ++x)
for (y = 0; y < MAX; ++y) pts[x][y] = ' ';
prev.x = prev.y = 0;
pts[0][0] = '.';
for (d = 1; d < N * N; ++d) {
d2pt(N, d, &curr);
cx = curr.x * K;
cy = curr.y * K;
px = prev.x * K;
py = prev.y * K;
pts[cx][cy] = '.';
if (cx == px ) {
if (py < cy)
for (y = py + 1; y < cy; ++y) pts[cx][y] = '|';
else
for (y = cy + 1; y < py; ++y) pts[cx][y] = '|';
}
else {
if (px < cx)
for (x = px + 1; x < cx; ++x) pts[x][cy] = '_';
else
for (x = cx + 1; x < px; ++x) pts[x][cy] = '_';
}
prev = curr;
}
for (x = 0; x < MAX; ++x) {
for (y = 0; y < MAX; ++y) printf("%c", pts[y][x]);
printf("\n");
}
return 0;
}</lang>
- Output:
Same as Kotlin entry.
C++
<lang cpp>#include <algorithm>
- include <iostream>
- include <vector>
struct Point {
int x, y;
//rotate/flip a quadrant appropriately
void rot(int n, bool rx, bool ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}
std::swap(x, y);
}
}
};
Point fromD(int n, int d) {
Point p = { 0, 0 };
bool rx, ry;
int t = d;
for (int s = 1; s < n; s <<= 1) {
rx = ((t & 2) != 0);
ry = (((t ^ (rx ? 1 : 0)) & 1) != 0);
p.rot(s, rx, ry);
p.x += (rx ? s : 0);
p.y += (ry ? s : 0);
t >>= 2;
}
return p;
}
std::vector<Point> getPointsForCurve(int n) {
std::vector<Point> points;
for (int d = 0; d < n * n; ++d) {
points.push_back(fromD(n, d));
}
return points;
}
std::vector<std::string> drawCurve(const std::vector<Point> &points, int n) {
auto canvas = new char *[n];
for (size_t i = 0; i < n; i++) {
canvas[i] = new char[n * 3 - 2];
std::memset(canvas[i], ' ', n * 3 - 2);
}
for (int i = 1; i < points.size(); i++) {
auto lastPoint = points[i - 1];
auto curPoint = points[i];
int deltaX = curPoint.x - lastPoint.x;
int deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
// vertical line
int row = std::max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row][col] = '|';
} else {
// horizontal line
int row = curPoint.y;
int col = std::min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row][col] = '_';
canvas[row][col + 1] = '_';
}
}
std::vector<std::string> lines;
for (size_t i = 0; i < n; i++) {
std::string temp;
temp.assign(canvas[i], n * 3 - 2);
lines.push_back(temp);
}
return lines;
}
int main() {
for (int order = 1; order < 6; order++) {
int n = 1 << order;
auto points = getPointsForCurve(n);
std::cout << "Hilbert curve, order=" << order << '\n';
auto lines = drawCurve(points, n);
for (auto &line : lines) {
std::cout << line << '\n';
}
std::cout << '\n';
}
return 0;
}</lang>
- Output:
Hilbert curve, order=1
|__|
Hilbert curve, order=2
__ __
__| |__
| __ |
|__| |__|
Hilbert curve, order=3
__ __ __ __
|__| __| |__ |__|
__ |__ __| __
| |__ __| |__ __| |
|__ __ __ __ __|
__| |__ __| |__
| __ | | __ |
|__| |__| |__| |__|
Hilbert curve, order=4
__ __ __ __ __ __ __ __ __ __
__| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__|
Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
|__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__|
__ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __
| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
C#
<lang csharp>using System; using System.Collections.Generic; using System.Diagnostics; using System.Text;
namespace HilbertCurve {
class Program {
static void Swap<T>(ref T a, ref T b) {
var c = a;
a = b;
b = c;
}
struct Point {
public int x, y;
public Point(int x, int y) {
this.x = x;
this.y = y;
}
//rotate/flip a quadrant appropriately
public void Rot(int n, bool rx, bool ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}
Swap(ref x, ref y);
}
}
public override string ToString() {
return string.Format("({0}, {1})", x, y);
}
}
static Point FromD(int n, int d) {
var p = new Point(0, 0);
int t = d;
for (int s = 1; s < n; s <<= 1) {
var rx = (t & 2) != 0;
var ry = ((t ^ (rx ? 1 : 0)) & 1) != 0;
p.Rot(s, rx, ry);
p.x += rx ? s : 0;
p.y += ry ? s : 0;
t >>= 2;
}
return p;
}
static List<Point> GetPointsForCurve(int n) {
var points = new List<Point>();
int d = 0;
while (d < n * n) {
points.Add(FromD(n, d));
d += 1;
}
return points;
}
static List<string> DrawCurve(List<Point> points, int n) {
var canvas = new char[n, n * 3 - 2];
for (int i = 0; i < canvas.GetLength(0); i++) {
for (int j = 0; j < canvas.GetLength(1); j++) {
canvas[i, j] = ' ';
}
}
for (int i = 1; i < points.Count; i++) {
var lastPoint = points[i - 1];
var curPoint = points[i];
var deltaX = curPoint.x - lastPoint.x;
var deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
Debug.Assert(deltaY != 0, "Duplicate point");
//vertical line
int row = Math.Max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row, col] = '|';
} else {
Debug.Assert(deltaY == 0, "Duplicate point");
//horizontal line
var row = curPoint.y;
var col = Math.Min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row, col] = '_';
canvas[row, col + 1] = '_';
}
}
var lines = new List<string>();
for (int i = 0; i < canvas.GetLength(0); i++) {
var sb = new StringBuilder();
for (int j = 0; j < canvas.GetLength(1); j++) {
sb.Append(canvas[i, j]);
}
lines.Add(sb.ToString());
}
return lines;
}
static void Main() {
for (int order = 1; order <= 5; order++) {
var n = 1 << order;
var points = GetPointsForCurve(n);
Console.WriteLine("Hilbert curve, order={0}", order);
var lines = DrawCurve(points, n);
foreach (var line in lines) {
Console.WriteLine(line);
}
Console.WriteLine();
}
}
}
}</lang>
- Output:
Hilbert curve, order=1
|__|
Hilbert curve, order=2
__ __
__| |__
| __ |
|__| |__|
Hilbert curve, order=3
__ __ __ __
|__| __| |__ |__|
__ |__ __| __
| |__ __| |__ __| |
|__ __ __ __ __|
__| |__ __| |__
| __ | | __ |
|__| |__| |__| |__|
Hilbert curve, order=4
__ __ __ __ __ __ __ __ __ __
__| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__|
Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
|__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__|
__ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __
| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
D
<lang d>import std.stdio;
void main() {
foreach (order; 1..6) {
int n = 1 << order;
auto points = getPointsForCurve(n);
writeln("Hilbert curve, order=", order);
auto lines = drawCurve(points, n);
foreach (line; lines) {
writeln(line);
}
writeln;
}
}
struct Point {
int x, y;
//rotate/flip a quadrant appropriately
void rot(int n, bool rx, bool ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}
import std.algorithm.mutation;
swap(x, y);
}
}
int calcD(int n) {
bool rx, ry;
int d;
for (int s = n >>> 1; s > 0; s >>>= 1) {
rx = ((x & s) != 0);
ry = ((y & s) != 0);
d += s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0));
rot(s, rx, ry);
}
return d;
}
void toString(scope void delegate(const(char)[]) sink) const {
import std.format : formattedWrite;
sink("(");
sink.formattedWrite!"%d"(x);
sink(", ");
sink.formattedWrite!"%d"(y);
sink(")");
}
}
auto fromD(int n, int d) {
Point p;
bool rx, ry;
int t = d;
for (int s = 1; s < n; s <<= 1) {
rx = ((t & 2) != 0);
ry = (((t ^ (rx ? 1 : 0)) & 1) != 0);
p.rot(s, rx, ry);
p.x += (rx ? s : 0);
p.y += (ry ? s : 0);
t >>>= 2;
}
return p;
}
auto getPointsForCurve(int n) {
Point[] points;
for (int d; d < n * n; ++d) {
points ~= fromD(n, d);
}
return points;
}
auto drawCurve(Point[] points, int n) {
import std.algorithm.comparison : min, max; import std.array : uninitializedArray; import std.exception : enforce;
auto canvas = uninitializedArray!(char[][])(n, n * 3 - 2);
foreach (line; canvas) {
line[] = ' ';
}
for (int i = 1; i < points.length; ++i) {
auto lastPoint = points[i - 1];
auto curPoint = points[i];
int deltaX = curPoint.x - lastPoint.x;
int deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
enforce(deltaY != 0, "Duplicate point");
// vertical line
int row = max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row][col] = '|';
} else {
enforce(deltaY == 0, "Diagonal line");
// horizontal line
int row = curPoint.y;
int col = min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row][col] = '_';
canvas[row][col + 1] = '_';
}
}
string[] lines;
foreach (row; canvas) {
lines ~= row.idup;
}
return lines;
}</lang>
- Output:
Hilbert curve, order=1
|__|
Hilbert curve, order=2
__ __
__| |__
| __ |
|__| |__|
Hilbert curve, order=3
__ __ __ __
|__| __| |__ |__|
__ |__ __| __
| |__ __| |__ __| |
|__ __ __ __ __|
__| |__ __| |__
| __ | | __ |
|__| |__| |__| |__|
Hilbert curve, order=4
__ __ __ __ __ __ __ __ __ __
__| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__|
Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
|__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__|
__ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __
| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
Fōrmulæ
In this page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
FreeBASIC
<lang freebasic> Dim Shared As Integer ancho = 64
Sub Hilbert(x As Integer, y As Integer, lg As Integer, i1 As Integer, i2 As Integer)
If lg = 1 Then
Line - ((ancho-x) * 10, (ancho-y) * 10)
Return
End If
lg = lg / 2
Hilbert(x+i1*lg, y+i1*lg, lg, i1, 1-i2)
Hilbert(x+i2*lg, y+(1-i2)*lg, lg, i1, i2)
Hilbert(x+(1-i1)*lg, y+(1-i1)*lg, lg, i1, i2)
Hilbert(x+(1-i2)*lg, y+i2*lg, lg, 1-i1, i2)
End Sub
Screenres 655, 655
Hilbert(0, 0, ancho, 0, 0) End </lang>
Go
The following is based on the recursive algorithm and C code in this paper. The image produced is similar to the one linked to in the zkl example.
<lang go>package main
import "github.com/fogleman/gg"
var points []gg.Point
const width = 64
func hilbert(x, y, lg, i1, i2 int) {
if lg == 1 {
px := float64(width-x) * 10
py := float64(width-y) * 10
points = append(points, gg.Point{px, py})
return
}
lg >>= 1
hilbert(x+i1*lg, y+i1*lg, lg, i1, 1-i2)
hilbert(x+i2*lg, y+(1-i2)*lg, lg, i1, i2)
hilbert(x+(1-i1)*lg, y+(1-i1)*lg, lg, i1, i2)
hilbert(x+(1-i2)*lg, y+i2*lg, lg, 1-i1, i2)
}
func main() {
hilbert(0, 0, width, 0, 0)
dc := gg.NewContext(650, 650)
dc.SetRGB(0, 0, 0) // Black background
dc.Clear()
for _, p := range points {
dc.LineTo(p.X, p.Y)
}
dc.SetHexColor("#90EE90") // Light green curve
dc.SetLineWidth(1)
dc.Stroke()
dc.SavePNG("hilbert.png")
}</lang>
Haskell
Defines an SVG string which can be rendered in a browser. A Hilbert tree is defined in terms of a production rule, and folded to a list of points in a square of given size.
<lang haskell>import Data.Bool (bool) import Data.Tree
rule :: Char -> String rule c =
case c of 'a' -> "daab" 'b' -> "cbba" 'c' -> "bccd" 'd' -> "addc" _ -> []
vectors :: Char -> [(Int, Int)] vectors c =
case c of 'a' -> [(-1, 1), (-1, -1), (1, -1), (1, 1)] 'b' -> [(1, -1), (-1, -1), (-1, 1), (1, 1)] 'c' -> [(1, -1), (1, 1), (-1, 1), (-1, -1)] 'd' -> [(-1, 1), (1, 1), (1, -1), (-1, -1)] _ -> []
main :: IO () main = do
let w = 1024 putStrLn $ svgFromPoints w $ hilbertPoints w (hilbertTree 6)
hilbertTree :: Int -> Tree Char hilbertTree n =
let go tree =
let c = rootLabel tree
xs = subForest tree
in Node c (bool (go <$> xs) (flip Node [] <$> rule c) (null xs))
seed = Node 'a' []
in bool seed (iterate go seed !! pred n) (0 < n)
hilbertPoints :: Int -> Tree Char -> [(Int, Int)] hilbertPoints w tree =
let go r xy tree =
let d = quot r 2
f g x = g xy + (d * g x)
centres = ((,) . f fst) <*> f snd <$> vectors (rootLabel tree)
xs = subForest tree
in bool (concat $ zipWith (go d) centres xs) centres (null xs)
r = quot w 2
in go r (r, r) tree
svgFromPoints :: Int -> [(Int, Int)] -> String svgFromPoints w xys =
let sw = show w
points =
(unwords . fmap (((++) . show . fst) <*> ((' ' :) . show . snd))) xys
in unlines
[ "<svg xmlns=\"http://www.w3.org/2000/svg\""
, unwords ["width=\"512\" height=\"512\" viewBox=\"5 5", sw, sw, "\"> "]
, "<path d=\"M" ++ points ++ "\" "
, "stroke-width=\"2\" stroke=\"red\" fill=\"transparent\"/>"
, "</svg>"
]</lang>
IS-BASIC
<lang IS-BASIC>100 PROGRAM "Hilbert.bas" 110 OPTION ANGLE DEGREES 120 GRAPHICS HIRES 2 130 LET N=5:LET P=1:LET S=11*2^(6-N) 140 PLOT 940,700,ANGLE 180; 150 CALL HILBERT(S,N,P) 160 DEF HILBERT(S,N,P) 170 IF N=0 THEN EXIT DEF 180 PLOT LEFT 90*P; 190 CALL HILBERT(S,N-1,-P) 200 PLOT FORWARD S;RIGHT 90*P; 210 CALL HILBERT(S,N-1,P) 220 PLOT FORWARD S; 230 CALL HILBERT(S,N-1,P) 240 PLOT RIGHT 90*P;FORWARD S; 250 CALL HILBERT(S,N-1,-P) 260 PLOT LEFT 90*P; 270 END DEF</lang>
Java
<lang java>// Translation from https://en.wikipedia.org/wiki/Hilbert_curve
import java.util.ArrayList; import java.util.Arrays; import java.util.List;
public class HilbertCurve {
public static class Point {
public int x;
public int y;
public Point(int x, int y) {
this.x = x;
this.y = y;
}
public String toString() {
return "(" + x + ", " + y + ")";
}
//rotate/flip a quadrant appropriately
public void rot(int n, boolean rx, boolean ry) {
if (!ry) {
if (rx) {
x = (n - 1) - x;
y = (n - 1) - y;
}
//Swap x and y
int t = x;
x = y;
y = t;
}
return;
}
public int calcD(int n) {
boolean rx, ry;
int d = 0;
for (int s = n >>> 1; s > 0; s >>>= 1) {
rx = ((x & s) != 0);
ry = ((y & s) != 0);
d += s * s * ((rx ? 3 : 0) ^ (ry ? 1 : 0));
rot(s, rx, ry);
}
return d;
}
}
public static Point fromD(int n, int d) {
Point p = new Point(0, 0);
boolean rx, ry;
int t = d;
for (int s = 1; s < n; s <<= 1) {
rx = ((t & 2) != 0);
ry = (((t ^ (rx ? 1 : 0)) & 1) != 0);
p.rot(s, rx, ry);
p.x += (rx ? s : 0);
p.y += (ry ? s : 0);
t >>>= 2;
}
return p;
}
public static List<Point> getPointsForCurve(int n) {
List<Point> points = new ArrayList<Point>();
for (int d = 0; d < (n * n); d++) {
Point p = fromD(n, d);
points.add(p);
}
return points;
}
public static List<String> drawCurve(List<Point> points, int n) {
char[][] canvas = new char[n][n * 3 - 2];
for (char[] line : canvas) {
Arrays.fill(line, ' ');
}
for (int i = 1; i < points.size(); i++) {
Point lastPoint = points.get(i - 1);
Point curPoint = points.get(i);
int deltaX = curPoint.x - lastPoint.x;
int deltaY = curPoint.y - lastPoint.y;
if (deltaX == 0) {
if (deltaY == 0) {
// A mistake has been made
throw new IllegalStateException("Duplicate point, deltaX=" + deltaX + ", deltaY=" + deltaY);
}
// Vertical line
int row = Math.max(curPoint.y, lastPoint.y);
int col = curPoint.x * 3;
canvas[row][col] = '|';
}
else {
if (deltaY != 0) {
// A mistake has been made
throw new IllegalStateException("Diagonal line, deltaX=" + deltaX + ", deltaY=" + deltaY);
}
// Horizontal line
int row = curPoint.y;
int col = Math.min(curPoint.x, lastPoint.x) * 3 + 1;
canvas[row][col] = '_';
canvas[row][col + 1] = '_';
}
}
List<String> lines = new ArrayList<String>();
for (char[] row : canvas) {
String line = new String(row);
lines.add(line);
}
return lines;
}
public static void main(String... args) {
for (int order = 1; order <= 5; order++) {
int n = (1 << order);
List<Point> points = getPointsForCurve(n);
System.out.println("Hilbert curve, order=" + order);
List<String> lines = drawCurve(points, n);
for (String line : lines) {
System.out.println(line);
}
System.out.println();
}
return;
}
}</lang>
- Output:
Hilbert curve, order=1
|__|
Hilbert curve, order=2
__ __
__| |__
| __ |
|__| |__|
Hilbert curve, order=3
__ __ __ __
|__| __| |__ |__|
__ |__ __| __
| |__ __| |__ __| |
|__ __ __ __ __|
__| |__ __| |__
| __ | | __ |
|__| |__| |__| |__|
Hilbert curve, order=4
__ __ __ __ __ __ __ __ __ __
__| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__|
Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
|__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__|
__ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __
| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
JavaScript
Imperative
An implementation of GO. Prints an SVG string that can be read in a browser. <lang javascript>const hilbert = (width, spacing, points) => (x, y, lg, i1, i2, f) => {
if (lg === 1) {
const px = (width - x) * spacing;
const py = (width - y) * spacing;
points.push(px, py);
return;
}
lg >>= 1;
f(x + i1 * lg, y + i1 * lg, lg, i1, 1 - i2, f);
f(x + i2 * lg, y + (1 - i2) * lg, lg, i1, i2, f);
f(x + (1 - i1) * lg, y + (1 - i1) * lg, lg, i1, i2, f);
f(x + (1 - i2) * lg, y + i2 * lg, lg, 1 - i1, i2, f);
return points;
};
/**
* Draw a hilbert curve of the given order.
* Outputs a svg string. Save the string as a .svg file and open in a browser.
* @param {!Number} order
*/
const drawHilbert = order => {
if (!order || order < 1) {
throw 'You need to give a valid positive integer';
} else {
order = Math.floor(order);
}
// Curve Constants const width = 2 ** order; const space = 10;
// SVG Setup const size = 500; const stroke = 2; const col = "red"; const fill = "transparent";
// Prep and run function
const f = hilbert(width, space, []);
const points = f(0, 0, width, 0, 0, f);
const path = points.join(' ');
console.log(
`<svg xmlns="http://www.w3.org/2000/svg"
width="${size}"
height="${size}"
viewBox="${space / 2} ${space / 2} ${width * space} ${width * space}">
<path d="M${path}" stroke-width="${stroke}" stroke="${col}" fill="${fill}"/>
</svg>`);
};
drawHilbert(6);</lang>
Functional
A composition of pure functions which defines a Hilbert tree as the Nth application of a production rule to a seedling tree.
A list of points is derived by serialization of that tree.
Like the version above, generates an SVG string for display in a browser.
<lang JavaScript>(() => {
'use strict';
const main = () => {
// rule :: Dict Char [Char]
const rule = {
a: ['d', 'a', 'a', 'b'],
b: ['c', 'b', 'b', 'a'],
c: ['b', 'c', 'c', 'd'],
d: ['a', 'd', 'd', 'c']
};
// vectors :: Dict Char [(Int, Int)]
const vectors = ({
'a': [
[-1, 1],
[-1, -1],
[1, -1],
[1, 1]
],
'b': [
[1, -1],
[-1, -1],
[-1, 1],
[1, 1]
],
'c': [
[1, -1],
[1, 1],
[-1, 1],
[-1, -1]
],
'd': [
[-1, 1],
[1, 1],
[1, -1],
[-1, -1]
]
});
// hilbertCurve :: Int -> SVG string
const hilbertCurve = n => {
const w = 1024
return svgFromPoints(w)(
hilbertPoints(w)(
hilbertTree(n)
)
);
}
// hilbertTree :: Int -> Tree Char
const hilbertTree = n => {
const go = tree =>
Node(
tree.root,
0 < tree.nest.length ? (
map(go, tree.nest)
) : map(x => Node(x, []), rule[tree.root])
);
const seed = Node('a', []);
return 0 < n ? (
take(n, iterate(go, seed)).slice(-1)[0]
) : seed;
};
// hilbertPoints :: Size -> Tree Char -> [(x, y)]
// hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
const hilbertPoints = w => tree => {
const go = d => (xy, tree) => {
const
r = Math.floor(d / 2),
centres = map(
v => [
xy[0] + (r * v[0]),
xy[1] + (r * v[1])
],
vectors[tree.root]
);
return 0 < tree.nest.length ? concat(
zipWith(go(r), centres, tree.nest)
) : centres;
};
const d = Math.floor(w / 2);
return go(d)([d, d], tree);
};
// svgFromPoints :: Int -> [(Int, Int)] -> String
const svgFromPoints = w => xys =>
['<svg xmlns="http://www.w3.org/2000/svg"',
`width="500" height="500" viewBox="5 5 ${w} ${w}">`,
`<path d="M${concat(xys).join(' ')}" `,
'stroke-width="2" stroke="red" fill="transparent"/>',
'</svg>'
].join('\n');
// TEST -------------------------------------------
console.log(
hilbertCurve(6)
);
};
// GENERIC FUNCTIONS ----------------------------------
// Node :: a -> [Tree a] -> Tree a
const Node = (v, xs) => ({
type: 'Node',
root: v, // any type of value (consistent across tree)
nest: xs || []
});
// concat :: a -> [a] // concat :: [String] -> String const concat = xs => 0 < xs.length ? (() => { const unit = 'string' !== typeof xs[0] ? ( [] ) : ; return unit.concat.apply(unit, xs); })() : [];
// iterate :: (a -> a) -> a -> Gen [a]
function* iterate(f, x) {
let v = x;
while (true) {
yield(v);
v = f(v);
}
}
// Returns Infinity over objects without finite length. // This enables zip and zipWith to choose the shorter // argument when one is non-finite, like cycle, repeat etc
// length :: [a] -> Int
const length = xs =>
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) =>
(Array.isArray(xs) ? (
xs
) : xs.split()).map(f);
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// Use of `take` and `length` here allows zipping with non-finite lists // i.e. generators like cycle, repeat, iterate.
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) => {
const
lng = Math.min(length(xs), length(ys)),
as = take(lng, xs),
bs = take(lng, ys);
return Array.from({
length: lng
}, (_, i) => f(as[i], bs[i], i));
};
// MAIN --- return main();
})();</lang>
Julia
Color graphics version using the Gtk package. <lang julia>using Gtk, Graphics, Colors
Base.isless(p1::Vec2, p2::Vec2) = (p1.x == p2.x ? p1.y < p2.y : p1.x < p2.x)
struct Line p1::Point p2::Point end
dist(p1, p2) = sqrt((p2.y - p1.y)^2 + (p2.x - p1.x)^2) length(ln::Line) = dist(ln.p1, ln.p2) isvertical(line) = (line.p1.x == line.p2.x) ishorizontal(line) = (line.p1.y == line.p2.y)
const colorseq = [colorant"blue", colorant"red", colorant"green"] const linewidth = 1 const toporder = 3
function drawline(ctx, p1, p2, color, width)
move_to(ctx, p1.x, p1.y) set_source(ctx, color) line_to(ctx, p2.x, p2.y) set_line_width(ctx, width) stroke(ctx)
end drawline(ctx, line, color, width=linewidth) = drawline(ctx, line.p1, line.p2, color, width)
function hilbertmutateboxes(ctx, line, order, maxorder=toporder)
if line.p1 < line.p2
p1, p2 = line.p1, line.p2
else
p2, p1 = line.p1, line.p2
end
color = colorseq[order % 3 + 1]
d = dist(p1, p2) / 3
if ishorizontal(line)
pl = Point(p1.x + d, p1.y)
plu = Point(p1.x + d, p1.y - d)
pld = Point(p1.x + d, p1.y + d)
pr = Point(p2.x - d, p2.y)
pru = Point(p2.x - d, p2.y - d)
prd = Point(p2.x - d, p2.y + d)
lines = [Line(plu, pl), Line(plu, pru), Line(pru, pr),
Line(pr, prd), Line(pld, prd), Line(pld, pl)]
else # vertical
pu = Point(p1.x, p1.y + d)
pul = Point(p1.x - d, p1.y + d)
pur = Point(p1.x + d, p1.y + d)
pd = Point(p2.x, p2.y - d)
pdl = Point(p2.x - d, p2.y - d)
pdr = Point(p2.x + d, p2.y - d)
lines = [Line(pul, pu), Line(pul, pdl), Line(pdl, pd),
Line(pu, pur), Line(pur, pdr), Line(pd, pdr)]
end
for li in lines
drawline(ctx, li, color)
end
if order <= maxorder
for li in lines
hilbertmutateboxes(ctx, li, order + 1, maxorder)
end
end
end
const can = @GtkCanvas()
const win = GtkWindow(can, "Hilbert 2D", 400, 400)
@guarded draw(can) do widget
ctx = getgc(can) h = height(can) w = width(can) line = Line(Point(0, h/2), Point(w, h/2)) drawline(ctx, line, colorant"black", 2) hilbertmutateboxes(ctx, line, 0)
end
show(can)
const cond = Condition()
endit(w) = notify(cond)
signal_connect(endit, win, :destroy)
wait(cond)
</lang>
Kotlin
Terminal drawing using ASCII characters within a 96 x 96 grid - starts at top left, ends at top right.
The coordinates of the points are generated using a translation of the C code in the Wikipedia article and then scaled by a factor of 3 (n = 32). <lang scala>// Version 1.2.40
data class Point(var x: Int, var y: Int)
fun d2pt(n: Int, d: Int): Point {
var x = 0
var y = 0
var t = d
var s = 1
while (s < n) {
val rx = 1 and (t / 2)
val ry = 1 and (t xor rx)
val p = Point(x, y)
rot(s, p, rx, ry)
x = p.x + s * rx
y = p.y + s * ry
t /= 4
s *= 2
}
return Point(x, y)
}
fun rot(n: Int, p: Point, rx: Int, ry: Int) {
if (ry == 0) {
if (rx == 1) {
p.x = n - 1 - p.x
p.y = n - 1 - p.y
}
val t = p.x
p.x = p.y
p.y = t
}
}
fun main(args:Array<String>) {
val n = 32
val k = 3
val pts = List(n * k) { CharArray(n * k) { ' ' } }
var prev = Point(0, 0)
pts[0][0] = '.'
for (d in 1 until n * n) {
val curr = d2pt(n, d)
val cx = curr.x * k
val cy = curr.y * k
val px = prev.x * k
val py = prev.y * k
pts[cx][cy] = '.'
if (cx == px ) {
if (py < cy)
for (y in py + 1 until cy) pts[cx][y] = '|'
else
for (y in cy + 1 until py) pts[cx][y] = '|'
}
else {
if (px < cx)
for (x in px + 1 until cx) pts[x][cy] = '_'
else
for (x in cx + 1 until px) pts[x][cy] = '_'
}
prev = curr
}
for (i in 0 until n * k) {
for (j in 0 until n * k) print(pts[j][i])
println()
}
}</lang>
- Output:
. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .
| | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | |
| | | | | | | | | |
.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | |
. .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. .
| | | | | |
| | | | | |
.__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__.
| | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
| | | | | | | | | | | | | |
| | | | | | | | | | | | | |
. .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. .
| | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__.
| |
| |
.__. .__. .__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | |
. .__. . . .__. . .__. .__. .__. .__. .__. .__. .__. .__. . .__. . . .__. .
| | | | | | | | | | | | | |
| | | | | | | | | | | | | |
.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | |
.__. .__.__.__. .__. .__. .__. . .__.__. .__.__. . .__. .__. .__. .__.__.__. .__.
| | | | | |
| | | | | |
. .__.__. .__.__. . .__. .__. . .__.__. .__.__. . .__. .__. . .__.__. .__.__. .
| | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. . .__. . .__. .__. .__. .__. . .__. . .__. .__. .__. .__.
| | | | | | | | | |
| | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | |
. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .__.__. .
| |
| |
.__. .__.__. .__.__. .__.__. .__.__. .__.__.__. .__.__. .__.__. .__.__. .__.__. .__.
| | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | | | |
| | | | | | | | | | | |
. .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. .
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
.__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__.
| | | |
| | | |
.__. .__. . .__.__. .__.__. . .__. .__. .__. .__. . .__.__. .__.__. . .__. .__.
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | |
. .__. . .__. .__. .__. .__. . .__. . . .__. . .__. .__. .__. .__. . .__. .
| | | | | | | | | | | |
| | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | |
.__. .__.__. .__.__. .__.__. .__.__. .__. .__. .__.__. .__.__. .__.__. .__.__. .__.
| | | |
| | | |
. .__.__. .__.__. .__. .__.__. .__.__. . . .__.__. .__.__. .__. .__.__. .__.__. .
| | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | |
| | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | |
. .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. . . .__.__. .__.__. .
| | | | | | | |
| | | | | | | |
.__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__. .__. .__.__.__. .__.
| | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
| | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | |
. .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. . . .__. .
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
.__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__. .__.
Lua
Solved by using the Lindenmayer path, printed with Unicode, which does not show perfectly on web, but is quite nice on console. Should work with all Lua versions, used nothing special. Should work up to Hilbert(12) if your console is big enough for that.
Implemented a full line-drawing Unicode/ASCII drawing and added for the example my signature to the default axiom "A" for fun and a second Hilbert "A" at the end, because it's looking better in the display like that. The implementation of repeated commands was just an additional line of code, so why not?
Lindenmayer:
- A,B are Lindenmayer AXIOMS
Line drawing:
- +,- turn right, left
- F draw line forward
- <num> repeat the following draw command <num> times
- <any> move on canvas without drawing
<lang lua>-- any version from LuaJIT 2.0/5.1, Lua 5.2, Lua 5.3 to LuaJIT 2.1.0-beta3-readline local bit=bit32 or bit -- Lua 5.2/5.3 compatibilty -- Hilbert curve implemented by Lindenmayer system function string.hilbert(s, n) for i=1,n do s=s:gsub("[AB]",function(c) if c=="A" then c="-BF+AFA+FB-" else c="+AF-BFB-FA+" end return c end) end s=s:gsub("[AB]",""):gsub("%+%-",""):gsub("%-%+","") return s end -- Or the characters for ASCII line drawing function charor(c1, c2) local bits={ [" "]=0x0, ["╷"]=0x1, ["╶"]=0x2, ["┌"]=0x3, ["╵"]=0x4, ["│"]=0x5, ["└"]=0x6, ["├"]=0x7, ["╴"]=0x8, ["┐"]=0x9, ["─"]=0xa, ["┬"]=0xb, ["┘"]=0xc, ["┤"]=0xd, ["┴"]=0xe, ["┼"]=0xf,} local char={" ", "╷", "╶", "┌", "╵", "│", "└", "├", "╴", "┐", "─", "┬", "┘", "┤", "┴", "┼",} local b1,b2=bits[c1] or 0,bits[c2] or 0 return char[bit.bor(b1,b2)+1] end -- ASCII line drawing routine function draw(s) local char={ {"─","┘","╴","┐",}, -- r {"│","┐","╷","┌",}, -- up {"─","┌","╶","└",}, -- l {"│","└","╵","┘",}, -- down } local scr={} local move={{x=1,y=0},{x=0,y=1},{x=-1,y=0},{x=0,y=-1}} local x,y=1,1 local minx,maxx,miny,maxy=1,1,1,1 local dir,turn=0,0 s=s.."F" local rep=0 for c in s:gmatch(".") do if c=="F" then repeat if scr[y]==nil then scr[y]={} end scr[y][x]=charor(char[dir+1][turn%#char[1]+1],scr[y][x] or " ") dir = (dir+turn) % #move x, y = x+move[dir+1].x,y+move[dir+1].y maxx,maxy=math.max(maxx,x),math.max(maxy,y) minx,miny=math.min(minx,x),math.min(miny,y) turn=0 rep=rep>1 and rep-1 or 0 until rep==0 elseif c=="-" then repeat turn=turn+1 rep=rep>1 and rep-1 or 0 until rep==0 elseif c=="+" then repeat turn=turn-1 rep=rep>1 and rep-1 or 0 until rep==0 elseif c:match("%d") then -- allow repeated commands rep=rep*10+tonumber(c) else repeat x, y = x+move[dir+1].x,y+move[dir+1].y maxx,maxy=math.max(maxx,x),math.max(maxy,y) minx,miny=math.min(minx,x),math.min(miny,y) rep=rep>1 and rep-1 or 0 until rep==0 end end for i=maxy,miny,-1 do local oneline={} for x=minx,maxx do oneline[1+x-minx]=scr[i] and scr[i][x] or " " end local line=table.concat(oneline) io.write(line, "\n") end end -- MAIN -- local n=arg[1] and tonumber(arg[1]) or 3 local str=arg[2] or "A" draw(str:hilbert(n)) </lang>
- Output:
luajit hilbert.lua 4 1M9FAF-4F2+2F-2F-2F++4F-F-4F+2F+2F+2F++3F+2F+3F--4FA10F-16F-58F-16F-
┌─────────────────────────────────────────────────────────┐ │ ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐ ┌┐┌┐┌┐┌┐┌┐┌┐┌┐┌┐ │ │ │└┘││└┘││└┘││└┘│ │└┘││└┘││└┘││└┘│ │ │ └┐┌┘└┐┌┘└┐┌┘└┐┌┘ └┐┌┘└┐┌┘└┐┌┘└┐┌┘ │ │ ┌┘└──┘└┐┌┘└──┘└┐ ┌┘└──┘└┐┌┘└──┘└┐ │ │ │┌─┐┌─┐││┌─┐┌─┐│ │┌─┐┌─┐││┌─┐┌─┐│ │ │ └┘┌┘└┐└┘└┘┌┘└┐└┘ └┘┌┘└┐└┘└┘┌┘└┐└┘ │ │ ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐ ┌┐└┐┌┘┌┐┌┐└┐┌┘┌┐ │ │ │└─┘└─┘└┘└─┘└─┘│ │└─┘└─┘└┘└─┘└─┘│ │ │ └┐┌─┐┌─┐┌─┐┌─┐┌┘ └┐┌─┐┌─┐┌─┐┌─┐┌┘ │ │ ┌┘└┐└┘┌┘└┐└┘┌┘└┐ ┌┘└┐└┘┌┘└┐└┘┌┘└┐ │ │ │┌┐│┌┐└┐┌┘┌┐│┌┐│ │┌┐│┌┐└┐┌┘┌┐│┌┐│ │ │ └┘└┘│└─┘└─┘│└┘└┘╷ ╷┌─┐ └┘└┘│└─┘└─┘│└┘└┘ │ │ ┌┐┌┐│┌─┐┌─┐│┌┐┌┐│ ││ │ ┌┐┌┐│┌─┐┌─┐│┌┐┌┐ │ │ │└┘│└┘┌┘└┐└┘│└┘│├─┤├─┴┐│└┘│└┘┌┘└┐└┘│└┘│ │ │ └┐┌┘┌┐└┐┌┘┌┐└┐┌┘│ ││ │└┐┌┘┌┐└┐┌┘┌┐└┐┌┘ │ └──────────┘└─┘└─┘└─┘└─┘└─┘ └┴──┴─┘└─┘└─┘└─┘└─┘└──────────┘
Mathematica
Works with: Mathematica 11 <lang Mathematica>Graphics@HilbertCurve[4]</lang>
Perl
<lang perl>use SVG; use List::Util qw(max min);
use constant pi => 2 * atan2(1, 0);
- Compute the curve with a Lindemayer-system
%rules = (
A => '-BF+AFA+FB-', B => '+AF-BFB-FA+'
); $hilbert = 'A'; $hilbert =~ s/([AB])/$rules{$1}/eg for 1..6;
- Draw the curve in SVG
($x, $y) = (0, 0); $theta = pi/2; $r = 5;
for (split //, $hilbert) {
if (/F/) {
push @X, sprintf "%.0f", $x;
push @Y, sprintf "%.0f", $y;
$x += $r * cos($theta);
$y += $r * sin($theta);
}
elsif (/\+/) { $theta += pi/2; }
elsif (/\-/) { $theta -= pi/2; }
}
$max = max(@X,@Y); $xt = -min(@X)+10; $yt = -min(@Y)+10; $svg = SVG->new(width=>$max+20, height=>$max+20); $points = $svg->get_path(x=>\@X, y=>\@Y, -type=>'polyline'); $svg->rect(width=>"100%", height=>"100%", style=>{'fill'=>'black'}); $svg->polyline(%$points, style=>{'stroke'=>'orange', 'stroke-width'=>1}, transform=>"translate($xt,$yt)");
open $fh, '>', 'hilbert_curve.svg'; print $fh $svg->xmlify(-namespace=>'svg'); close $fh;</lang> Hilbert curve (offsite image)
Perl 6
<lang perl6>use SVG;
role Lindenmayer {
has %.rules;
method succ {
self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)
}
}
my $hilbert = 'A' but Lindenmayer( { A => '-BF+AFA+FB-', B => '+AF-BFB-FA+' } );
$hilbert++ xx 7; my @points = (647, 13);
for $hilbert.comb {
state ($x, $y) = @points[0,1];
state $d = -5 - 0i;
when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) }
when /< + - >/ { $d *= "{$_}1i" }
default { }
}
say SVG.serialize(
svg => [
:660width, :660height, :style<stroke:blue>,
:rect[:width<100%>, :height<100%>, :fill<white>],
:polyline[ :points(@points.join: ','), :fill<white> ],
],
);</lang> See: Hilbert curve
There is a variation of a Hilbert curve known as a Moore curve which is essentially 4 Hilbert curves joined together in a loop. <lang perl6>use SVG;
role Lindenmayer {
has %.rules;
method succ {
self.comb.map( { %!rules{$^c} // $c } ).join but Lindenmayer(%!rules)
}
}
my $moore = 'AFA+F+AFA' but Lindenmayer( { A => '-BF+AFA+FB-', B => '+AF-BFB-FA+' } );
$moore++ xx 6; my @points = (327, 647);
for $moore.comb {
state ($x, $y) = @points[0,1];
state $d = 0 - 5i;
when 'F' { @points.append: ($x += $d.re).round(1), ($y += $d.im).round(1) }
when /< + - >/ { $d *= "{$_}1i" }
default { }
}
say SVG.serialize(
svg => [
:660width, :660height, :style<stroke:darkviolet>,
:rect[:width<100%>, :height<100%>, :fill<white>],
:polyline[ :points(@points.join: ','), :fill<white> ],
],
);</lang> See: Moore curve
Phix
<lang Phix>-- demo\rosetta\hilbert_curve.exw include pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
constant width = 64
sequence points = {}
procedure hilbert(integer x, y, lg, i1, i2)
if lg=1 then
integer px := (width-x) * 10,
py := (width-y) * 10
points = append(points, {px, py})
return
end if
lg /= 2
hilbert(x+i1*lg, y+i1*lg, lg, i1, 1-i2)
hilbert(x+i2*lg, y+(1-i2)*lg, lg, i1, i2)
hilbert(x+(1-i1)*lg, y+(1-i1)*lg, lg, i1, i2)
hilbert(x+(1-i2)*lg, y+i2*lg, lg, 1-i1, i2)
end procedure
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
cdCanvasBegin(cddbuffer, CD_OPEN_LINES)
for i=1 to length(points) do
integer {x,y} = points[i]
cdCanvasVertex(cddbuffer, x, y)
end for
cdCanvasEnd(cddbuffer)
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_WHITE) cdCanvasSetForeground(cddbuffer, CD_MAGENTA) return IUP_DEFAULT
end function
procedure main()
hilbert(0, 0, width, 0, 0)
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "655x655")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Hilbert Curve")
IupSetAttribute(dlg, "DIALOGFRAME", "YES") -- no resize here
IupCloseOnEscape(dlg)
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg)
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure main()</lang>
Python
Functional
Composition of pure functions, with type comments for the reader rather than the compiler.
An SVG path is serialised from the Nth application of re-write rules to a Hilbert tree structure.
(To view the Hilbert curve, save the output SVG text in a file with an appropriate extension (e.g. .svg), and open it with a browser).
<lang Python>Hilbert curve
from itertools import (chain, islice, starmap) from inspect import signature
- hilbertCurve :: Int -> SVG String
def hilbertCurve(n):
An SVG string representing a
Hilbert curve of degree n.
w = 1024
return svgFromPoints(w)(
hilbertPoints(w)(
hilbertTree(n)
)
)
- hilbertTree :: Int -> Tree Char
def hilbertTree(n):
Nth application of a rule to a seedling tree.
# rule :: Dict Char [Char]
rule = {
'a': ['d', 'a', 'a', 'b'],
'b': ['c', 'b', 'b', 'a'],
'c': ['b', 'c', 'c', 'd'],
'd': ['a', 'd', 'd', 'c']
}
# go :: Tree Char -> Tree Char
def go(tree):
c = tree['root']
xs = tree['nest']
return Node(c)(
map(go, xs) if xs else map(
flip(Node)([]),
rule[c]
)
)
seed = Node('a')([])
return list(islice(
iterate(go)(seed), n
))[-1] if 0 < n else seed
- hilbertPoints :: Int -> Tree Char -> [(Int, Int)]
def hilbertPoints(w):
Serialization of a tree to a list of points
bounded by a square of side w.
# vectors :: Dict Char [(Int, Int)]
vectors = {
'a': [(-1, 1), (-1, -1), (1, -1), (1, 1)],
'b': [(1, -1), (-1, -1), (-1, 1), (1, 1)],
'c': [(1, -1), (1, 1), (-1, 1), (-1, -1)],
'd': [(-1, 1), (1, 1), (1, -1), (-1, -1)]
}
# points :: Int -> ((Int, Int), Tree Char) -> [(Int, Int)]
def points(d):
Size -> Centre of a Hilbert subtree -> All subtree points
def go(xy, tree):
r = d // 2
centres = map(
lambda v: (
xy[0] + (r * v[0]),
xy[1] + (r * v[1])
),
vectors[tree['root']]
)
return chain.from_iterable(
starmap(points(r), zip(centres, tree['nest']))
) if tree['nest'] else centres
return lambda xy, tree: go(xy, tree)
d = w // 2 return lambda tree: list(points(d)((d, d), tree))
- svgFromPoints :: Int -> [(Int, Int)] -> SVG String
def svgFromPoints(w):
Width of square canvas -> Point list -> SVG string
def go(w, xys):
xs = ' '.join(map(
lambda xy: str(xy[0]) + ' ' + str(xy[1]),
xys
))
return '\n'.join(
['<svg xmlns="http://www.w3.org/2000/svg"',
f'width="512" height="512" viewBox="5 5 {w} {w}">',
f'<path d="M{xs}" ',
'stroke-width="2" stroke="red" fill="transparent"/>',
'</svg>'
]
)
return lambda xys: go(w, xys)
- TEST ----------------------------------------------------
def main():
Testing generation of the SVG for a Hilbert curve
print(
hilbertCurve(6)
)
- GENERIC FUNCTIONS ---------------------------------------
- Node :: a -> [Tree a] -> Tree a
def Node(v):
Contructor for a Tree node which connects a
value of some kind to a list of zero or
more child trees.
return lambda xs: {'type': 'Node', 'root': v, 'nest': xs}
- flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
The (curried or uncurried) function f with its
arguments reversed.
if 1 < len(signature(f).parameters):
return lambda a, b: f(b, a)
else:
return lambda a: lambda b: f(b)(a)
- iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
An infinite list of repeated
applications of f to x.
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)
- TEST ---------------------------------------------------
if __name__ == '__main__':
main()</lang>
Recursive
<lang Python> import matplotlib.pyplot as plt import numpy as np import turtle as tt
- dictionary containing the first order hilbert curves
base_shape = {'u': [np.array([0, 1]), np.array([1, 0]), np.array([0, -1])],
'd': [np.array([0, -1]), np.array([-1, 0]), np.array([0, 1])],
'r': [np.array([1, 0]), np.array([0, 1]), np.array([-1, 0])],
'l': [np.array([-1, 0]), np.array([0, -1]), np.array([1, 0])]}
def hilbert_curve(order, orientation):
"""
Recursively creates the structure for a hilbert curve of given order
"""
if order > 1:
if orientation == 'u':
return hilbert_curve(order - 1, 'r') + [np.array([0, 1])] + \
hilbert_curve(order - 1, 'u') + [np.array([1, 0])] + \
hilbert_curve(order - 1, 'u') + [np.array([0, -1])] + \
hilbert_curve(order - 1, 'l')
elif orientation == 'd':
return hilbert_curve(order - 1, 'l') + [np.array([0, -1])] + \
hilbert_curve(order - 1, 'd') + [np.array([-1, 0])] + \
hilbert_curve(order - 1, 'd') + [np.array([0, 1])] + \
hilbert_curve(order - 1, 'r')
elif orientation == 'r':
return hilbert_curve(order - 1, 'u') + [np.array([1, 0])] + \
hilbert_curve(order - 1, 'r') + [np.array([0, 1])] + \
hilbert_curve(order - 1, 'r') + [np.array([-1, 0])] + \
hilbert_curve(order - 1, 'd')
else:
return hilbert_curve(order - 1, 'd') + [np.array([-1, 0])] + \
hilbert_curve(order - 1, 'l') + [np.array([0, -1])] + \
hilbert_curve(order - 1, 'l') + [np.array([1, 0])] + \
hilbert_curve(order - 1, 'u')
else:
return base_shape[orientation]
- test the functions
if __name__ == '__main__':
order = 8
curve = hilbert_curve(order, 'u')
curve = np.array(curve) * 4
cumulative_curve = np.array([np.sum(curve[:i], 0) for i in range(len(curve)+1)])
# plot curve using plt
plt.plot(cumulative_curve[:, 0], cumulative_curve[:, 1])
# draw curve using turtle graphics
tt.setup(1920, 1000)
tt.pu()
tt.goto(-950, -490)
tt.pd()
tt.speed(0)
for item in curve:
tt.goto(tt.pos()[0] + item[0], tt.pos()[1] + item[1])
tt.done()
</lang>
Ring
<lang ring>
- Project : Hilbert curve
load "guilib.ring"
paint = null x1 = 0 y1 = 0
new qapp
{
win1 = new qwidget() {
setwindowtitle("Hilbert curve")
setgeometry(100,100,400,500)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,400,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
x1 = 0.5
y1 = 0.5
hilbert(0, 0, 200, 0, 0, 200, 4)
endpaint()
}
label1 { setpicture(p1) show() }
func hilbert (x, y, xi, xj, yi, yj, n)
cur = new QCursor() {
setpos(100, 100)
}
if (n <= 0)
drawtoline(x + (xi + yi)/2, y + (xj + yj)/2)
else
hilbert(x, y, yi/2, yj/2, xi/2, xj/2, n-1)
hilbert(x+xi/2, y+xj/2 , xi/2, xj/2, yi/2, yj/2, n-1)
hilbert(x+xi/2+yi/2, y+xj/2+yj/2, xi/2, xj/2, yi/2, yj/2, n-1);
hilbert(x+xi/2+yi, y+xj/2+yj, -yi/2,-yj/2, -xi/2, -xj/2, n-1)
ok
func drawtoline x2, y2
paint.drawline(x1, y1, x2, y2)
x1 = x2
y1 = y2
</lang> Output image: Hilbert curve
Racket
<lang racket>#lang racket
(require racket/draw)
(define rules '([A . (- B F + A F A + F B -)]
[B . (+ A F - B F B - F A +)]))
(define (get-cmds n cmd)
(cond
[(= 0 n) (list cmd)]
[else (append-map (curry get-cmds (sub1 n))
(dict-ref rules cmd (list cmd)))]))
(define (make-curve DIM N R OFFSET COLOR BACKGROUND-COLOR)
(define target (make-bitmap DIM DIM))
(define dc (new bitmap-dc% [bitmap target]))
(send dc set-background BACKGROUND-COLOR)
(send dc set-pen COLOR 1 'solid)
(send dc clear)
(for/fold ([x 0] [y 0] [θ (/ pi 2)])
([cmd (in-list (get-cmds N 'A))])
(define (draw/values x* y* θ*)
(send/apply dc draw-line (map (curry + OFFSET) (list x y x* y*)))
(values x* y* θ*))
(match cmd
['F (draw/values (+ x (* R (cos θ))) (+ y (* R (sin θ))) θ)]
['+ (values x y (+ θ (/ pi 2)))]
['- (values x y (- θ (/ pi 2)))]
[_ (values x y θ)]))
target)
(make-curve 500 6 7 30 (make-color 255 255 0) (make-color 0 0 0))</lang>
Ruby
Implemented as a Lindenmayer System, depends on JRuby or JRubyComplete
<lang Ruby>
- frozen_string_literal: true
attr_reader :hilbert def settings
size 600, 600
end
def setup
sketch_title '2D Hilbert' @hilbert = Hilbert.new hilbert.create_grammar 5 no_loop
end
def draw
background 0 hilbert.render
end
class Grammar
attr_reader :axiom, :rules def initialize(axiom, rules) @axiom = axiom @rules = rules end
def apply_rules(prod)
prod.gsub(/./) { |token| rules.fetch(token, token) }
end
def generate(gen) return axiom if gen.zero?
prod = axiom
gen.times do
prod = apply_rules(prod)
end
prod
end
end
Turtle = Struct.new(:x, :y, :theta)
- Hilbert Class has access to Sketch methods eg :line, :width, :height
class Hilbert
include Processing::Proxy
attr_reader :grammar, :axiom, :draw_length, :production, :turtle
DELTA = 90.radians
def initialize
@axiom = 'FL'
@grammar = Grammar.new(
axiom,
'L' => '+RF-LFL-FR+',
'R' => '-LF+RFR+FL-'
)
@draw_length = 200
stroke 0, 255, 0
stroke_weight 2
@turtle = Turtle.new(width / 9, height / 9, 0)
end
def render
production.scan(/./) do |element|
case element
when 'F' # NB NOT using affine transforms
draw_line(turtle)
when '+'
turtle.theta += DELTA
when '-'
turtle.theta -= DELTA
when 'L'
when 'R'
else puts 'Grammar not recognized'
end
end
end
def draw_line(turtle) x_temp = turtle.x y_temp = turtle.y turtle.x += draw_length * Math.cos(turtle.theta) turtle.y += draw_length * Math.sin(turtle.theta) line(x_temp, y_temp, turtle.x, turtle.y) end
############################## # create grammar from axiom and # rules (adjust scale) ##############################
def create_grammar(gen) @draw_length *= 0.6**gen @production = @grammar.generate gen end
end </lang>
Scala
Scala.js
<lang Scala>@js.annotation.JSExportTopLevel("ScalaFiddle") object ScalaFiddle {
// $FiddleStart import scala.util.Random
case class Point(x: Int, y: Int)
def xy2d(order: Int, d: Int): Point = {
def rot(order: Int, p: Point, rx: Int, ry: Int): Point = {
val np = if (rx == 1) Point(order - 1 - p.x, order - 1 - p.y) else p
if (ry == 0) Point(np.y, np.x) else p
}
@scala.annotation.tailrec
def iter(rx: Int, ry: Int, s: Int, t: Int, p: Point): Point = {
if (s < order) {
val _rx = 1 & (t / 2)
val _ry = 1 & (t ^ _rx)
val temp = rot(s, p, _rx, _ry)
iter(_rx, _ry, s * 2, t / 4, Point(temp.x + s * _rx, temp.y + s * _ry))
} else p
}
iter(0, 0, 1, d, Point(0, 0)) }
def randomColor =
s"rgb(${Random.nextInt(240)}, ${Random.nextInt(240)}, ${Random.nextInt(240)})"
val order = 64 val factor = math.min(Fiddle.canvas.height, Fiddle.canvas.width) / order.toDouble val maxD = order * order var d = 0 Fiddle.draw.strokeStyle = randomColor Fiddle.draw.lineWidth = 2 Fiddle.draw.lineCap = "square"
Fiddle.schedule(10) {
val h = xy2d(order, d)
Fiddle.draw.lineTo(h.x * factor, h.y * factor)
Fiddle.draw.stroke
if ({d += 1; d >= maxD})
{d = 1; Fiddle.draw.strokeStyle = randomColor}
Fiddle.draw.beginPath
Fiddle.draw.moveTo(h.x * factor, h.y * factor)
}
// $FiddleEnd
}</lang>
- Output:
Best seen running in your browser by ScalaFiddle (ES aka JavaScript, non JVM).
Seed7
<lang seed7>$ include "seed7_05.s7i";
include "draw.s7i"; include "keybd.s7i";
const integer: delta is 8;
const proc: drawDown (inout integer: x, inout integer: y, in integer: n) is forward; const proc: drawUp (inout integer: x, inout integer: y, in integer: n) is forward;
const proc: drawRight (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawDown(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawRight(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawRight(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawUp(x, y, pred(n));
end if;
end func;
const proc: drawLeft (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawUp(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawLeft(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawLeft(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawDown(x, y, pred(n));
end if;
end func;
const proc: drawDown (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawRight(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawDown(x, y, pred(n));
line(x, y, 0, delta, white);
y +:= delta;
drawDown(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawLeft(x, y, pred(n));
end if;
end func;
const proc: drawUp (inout integer: x, inout integer: y, in integer: n) is func
begin
if n > 0 then
drawLeft(x, y, pred(n));
line(x, y, -delta, 0, white);
x -:= delta;
drawUp(x, y, pred(n));
line(x, y, 0, -delta, white);
y -:= delta;
drawUp(x, y, pred(n));
line(x, y, delta, 0, white);
x +:= delta;
drawRight(x, y, pred(n));
end if;
end func;
const proc: main is func
local var integer: x is 11; var integer: y is 11; begin screen(526, 526); KEYBOARD := GRAPH_KEYBOARD; drawRight(x, y, 6); readln(KEYBOARD); end func;</lang>
Sidef
Generic implementation of the Lindenmayer system: <lang ruby>require('Image::Magick')
class Turtle(
x = 500, y = 500, angle = 0, scale = 1, mirror = 1, xoff = 0, yoff = 0, color = 'black',
) {
has im = %O<Image::Magick>.new(size => "#{x}x#{y}")
method init {
angle.deg2rad!
im.ReadImage('canvas:white')
}
method forward(r) {
var (newx, newy) = (x + r*sin(angle), y + r*-cos(angle))
im.Draw(
primitive => 'line',
points => join(' ',
round(x * scale + xoff),
round(y * scale + yoff),
round(newx * scale + xoff),
round(newy * scale + yoff),
),
stroke => color,
strokewidth => 1,
)
(x, y) = (newx, newy) }
method save_as(filename) {
im.Write(filename)
}
method turn(theta) {
angle += theta*mirror
}
method state {
[x, y, angle, mirror]
}
method setstate(state) {
(x, y, angle, mirror) = state...
}
method mirror {
mirror.neg!
}
}
class LSystem(
angle = 90, scale = 1, xoff = 0, yoff = 0, len = 5, color = 'black', width = 500, height = 500, turn = 0,
) {
has stack = [] has table = Hash()
has turtle = Turtle(
x: width,
y: height,
angle: turn,
scale: scale,
color: color,
xoff: xoff,
yoff: yoff,
)
method init {
angle.deg2rad!
turn.deg2rad!
table = Hash(
'+' => { turtle.turn(angle) },
'-' => { turtle.turn(-angle) },
':' => { turtle.mirror },
'[' => { stack.push(turtle.state) },
']' => { turtle.setstate(stack.pop) },
)
}
method execute(string, repetitions, filename, rules) {
repetitions.times {
string.gsub!(/(.)/, {|c| rules{c} \\ c })
}
string.each_char { |c|
if (table.contains(c)) {
table{c}.run
}
elsif (c.is_uppercase) {
turtle.forward(len)
}
}
turtle.save_as(filename) }
}</lang>
Generating the Hilbert curve: <lang ruby>var rules = Hash(
a => '-bF+aFa+Fb-', b => '+aF-bFb-Fa+',
)
var lsys = LSystem(
width: 600, height: 600,
xoff: -50, yoff: -50,
len: 8, angle: 90, color: 'dark green',
)
lsys.execute('a', 6, "hilbert_curve.png", rules)</lang> Output image: Hilbert curve
Vala
<lang vala>struct Point{
int x;
int y;
Point(int px,int py){
x=px;
y=py;
}
}
public class Hilbert : Gtk.DrawingArea {
private int it = 1; private Point[] points; private const int WINSIZE = 300;
public Hilbert() {
set_size_request(WINSIZE, WINSIZE);
}
public void button_toggled_cb(Gtk.ToggleButton button){
if(button.get_active()){
it = int.parse(button.get_label());
redraw_canvas();
}
}
public override bool draw(Cairo.Context cr){
int border_size = 20;
int unit = (WINSIZE - 2 * border_size)/((1<<it)-1);
//adjust border_size to center the drawing
border_size = border_size + (WINSIZE - 2 * border_size - unit * ((1<<it)-1)) / 2;
//white background
cr.rectangle(0, 0, WINSIZE, WINSIZE);
cr.set_source_rgb(1, 1, 1);
cr.fill_preserve();
cr.stroke();
points = {};
hilbert(0, 0, 1<<it, 0, 0);
//magenta lines
cr.set_source_rgb(1, 0, 1);
// move to first point
Point point = translate(border_size, WINSIZE, unit*points[0].x, unit*points[0].y);
cr.move_to(point.x, point.y);
foreach(Point i in points[1:points.length]){
point = translate(border_size, WINSIZE, unit*i.x, unit*i.y);
cr.line_to(point.x, point.y);
}
cr.stroke();
return false;
}
private Point translate(int border_size, int size, int x, int y){
return Point(border_size + x,size - border_size - y);
}
private void hilbert(int x, int y, int lg, int i1, int i2) {
if (lg == 1) {
points += Point(x,y);
return;
}
lg >>= 1;
hilbert(x+i1*lg, y+i1*lg, lg, i1, 1-i2);
hilbert(x+i2*lg, y+(1-i2)*lg, lg, i1, i2);
hilbert(x+(1-i1)*lg, y+(1-i1)*lg, lg, i1, i2);
hilbert(x+(1-i2)*lg, y+i2*lg, lg, 1-i1, i2);
}
private void redraw_canvas(){
var window = get_window();
if (window == null)return;
window.invalidate_region(window.get_clip_region(), true);
}
}
int main(string[] args){
Gtk.init (ref args);
var window = new Gtk.Window(); window.title = "Rosetta Code / Hilbert"; window.window_position = Gtk.WindowPosition.CENTER; window.destroy.connect(Gtk.main_quit); window.set_resizable(false);
var label = new Gtk.Label("Iterations:");
// create radio buttons to select the number of iterations
var rb1 = new Gtk.RadioButton(null);
rb1.set_label("1");
var rb2 = new Gtk.RadioButton.with_label_from_widget(rb1, "2");
var rb3 = new Gtk.RadioButton.with_label_from_widget(rb1, "3");
var rb4 = new Gtk.RadioButton.with_label_from_widget(rb1, "4");
var rb5 = new Gtk.RadioButton.with_label_from_widget(rb1, "5");
var hilbert = new Hilbert();
rb1.toggled.connect(hilbert.button_toggled_cb); rb2.toggled.connect(hilbert.button_toggled_cb); rb3.toggled.connect(hilbert.button_toggled_cb); rb4.toggled.connect(hilbert.button_toggled_cb); rb5.toggled.connect(hilbert.button_toggled_cb);
var box = new Gtk.Box(Gtk.Orientation.HORIZONTAL, 0); box.pack_start(label, false, false, 5); box.pack_start(rb1, false, false, 0); box.pack_start(rb2, false, false, 0); box.pack_start(rb3, false, false, 0); box.pack_start(rb4, false, false, 0); box.pack_start(rb5, false, false, 0);
var grid = new Gtk.Grid(); grid.attach(box, 0, 0, 1, 1); grid.attach(hilbert, 0, 1, 1, 1); grid.set_border_width(5); grid.set_row_spacing(5);
window.add(grid); window.show_all();
//initialise the drawing with iteration = 4 rb4.set_active(true);
Gtk.main(); return 0;
}</lang>
Visual Basic .NET
<lang vbnet>Imports System.Text
Module Module1
Sub Swap(Of T)(ByRef a As T, ByRef b As T)
Dim c = a
a = b
b = c
End Sub
Structure Point
Dim x As Integer
Dim y As Integer
'rotate/flip a quadrant appropriately
Sub Rot(n As Integer, rx As Boolean, ry As Boolean)
If Not ry Then
If rx Then
x = (n - 1) - x
y = (n - 1) - y
End If
Swap(x, y)
End If
End Sub
Public Overrides Function ToString() As String
Return String.Format("({0}, {1})", x, y)
End Function
End Structure
Function FromD(n As Integer, d As Integer) As Point
Dim p As Point
Dim rx As Boolean
Dim ry As Boolean
Dim t = d
Dim s = 1
While s < n
rx = ((t And 2) <> 0)
ry = (((t Xor If(rx, 1, 0)) And 1) <> 0)
p.Rot(s, rx, ry)
p.x += If(rx, s, 0)
p.y += If(ry, s, 0)
t >>= 2
s <<= 1
End While
Return p
End Function
Function GetPointsForCurve(n As Integer) As List(Of Point)
Dim points As New List(Of Point)
Dim d = 0
While d < n * n
points.Add(FromD(n, d))
d += 1
End While
Return points
End Function
Function DrawCurve(points As List(Of Point), n As Integer) As List(Of String)
Dim canvas(n, n * 3 - 2) As Char
For i = 1 To canvas.GetLength(0)
For j = 1 To canvas.GetLength(1)
canvas(i - 1, j - 1) = " "
Next
Next
For i = 1 To points.Count - 1
Dim lastPoint = points(i - 1)
Dim curPoint = points(i)
Dim deltaX = curPoint.x - lastPoint.x
Dim deltaY = curPoint.y - lastPoint.y
If deltaX = 0 Then
'vertical line
Dim row = Math.Max(curPoint.y, lastPoint.y)
Dim col = curPoint.x * 3
canvas(row, col) = "|"
Else
'horizontal line
Dim row = curPoint.y
Dim col = Math.Min(curPoint.x, lastPoint.x) * 3 + 1
canvas(row, col) = "_"
canvas(row, col + 1) = "_"
End If
Next
Dim lines As New List(Of String)
For i = 1 To canvas.GetLength(0)
Dim sb As New StringBuilder
For j = 1 To canvas.GetLength(1)
sb.Append(canvas(i - 1, j - 1))
Next
lines.Add(sb.ToString())
Next
Return lines
End Function
Sub Main()
For order = 1 To 5
Dim n = 1 << order
Dim points = GetPointsForCurve(n)
Console.WriteLine("Hilbert curve, order={0}", order)
Dim lines = DrawCurve(points, n)
For Each line In lines
Console.WriteLine(line)
Next
Console.WriteLine()
Next
End Sub
End Module</lang>
- Output:
Hilbert curve, order=1
|__|
Hilbert curve, order=2
__ __
__| |__
| __ |
|__| |__|
Hilbert curve, order=3
__ __ __ __
|__| __| |__ |__|
__ |__ __| __
| |__ __| |__ __| |
|__ __ __ __ __|
__| |__ __| |__
| __ | | __ |
|__| |__| |__| |__|
Hilbert curve, order=4
__ __ __ __ __ __ __ __ __ __
__| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__|
Hilbert curve, order=5
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__| __| |__ |__|
__ |__ __| __ | __ | __ |__ __| __ | __ | __ |__ __| __
| |__ __| |__ __| | |__| |__| | |__ __| |__ __| | |__| |__| | |__ __| |__ __| |
|__ __ __ __ __| __ __ | __ __ __ __ | __ __ |__ __ __ __ __|
__| |__ __| |__ | |__| | |__| __| |__ |__| | |__| | __| |__ __| |__
| __ | | __ | |__ __| __ |__ __| __ |__ __| | __ | | __ |
|__| |__| |__| |__| __| |__ __| |__ __| |__ __| |__ __| |__ |__| |__| |__| |__|
__ __ __ __ |__ __ __ __ __ __ __ __ __ __| __ __ __ __
| |__| | | |__| | __| |__ |__| __| |__ |__| __| |__ | |__| | | |__| |
|__ __| |__ __| | __ | __ |__ __| __ | __ | |__ __| |__ __|
__| |__ __ __| |__ |__| |__| | |__ __| |__ __| | |__| |__| __| |__ __ __| |__
| __ __ __ __ | __ __ | __ __ __ __ | __ __ | __ __ __ __ |
|__| __| |__ |__| | |__| | |__| __| |__ |__| | |__| | |__| __| |__ |__|
__ |__ __| __ |__ __| __ |__ __| __ |__ __| __ |__ __| __
| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |
|__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __|
__| |__ |__| __| |__ |__| __| |__ __| |__ |__| __| |__ |__| __| |__
| __ | __ |__ __| __ | __ | | __ | __ |__ __| __ | __ |
|__| |__| | |__ __| |__ __| | |__| |__| |__| |__| | |__ __| |__ __| | |__| |__|
__ __ | __ __ __ __ | __ __ __ __ | __ __ __ __ | __ __
| |__| | |__| __| |__ |__| | |__| | | |__| | |__| __| |__ |__| | |__| |
|__ __| __ |__ __| __ |__ __| |__ __| __ |__ __| __ |__ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ __ __ __ __ __ __ __ __ | | __ __ __ __ __ __ __ __ __ |
|__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__| |__| __| |__ |__|
__ |__ __| __ __ |__ __| __ __ |__ __| __ __ |__ __| __
| |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| | | |__ __| |__ __| |
|__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __| |__ __ __ __ __|
__| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__ __| |__
| __ | | __ | | __ | | __ | | __ | | __ | | __ | | __ |
|__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__| |__|
Yabasic
<lang Yabasic>width = 64
sub hilbert(x, y, lg, i1, i2)
if lg = 1 then
line to (width-x) * 10, (width-y) * 10
return
end if
lg = lg / 2
hilbert(x+i1*lg, y+i1*lg, lg, i1, 1-i2)
hilbert(x+i2*lg, y+(1-i2)*lg, lg, i1, i2)
hilbert(x+(1-i1)*lg, y+(1-i1)*lg, lg, i1, i2)
hilbert(x+(1-i2)*lg, y+i2*lg, lg, 1-i1, i2)
end sub
open window 655, 655
hilbert(0, 0, width, 0, 0)</lang>
zkl
Uses Image Magick and the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>hilbert(6) : turtle(_);
fcn hilbert(n){ // Lindenmayer system --> Data of As & Bs
var [const] A="-BF+AFA+FB-", B="+AF-BFB-FA+";
buf1,buf2 := Data(Void,"A").howza(3), Data().howza(3); // characters
do(n){
buf1.pump(buf2.clear(),fcn(c){ if(c=="A") A else if(c=="B") B else c });
t:=buf1; buf1=buf2; buf2=t; // swap buffers
}
buf1 // n=6 --> 13,651 letters
}
fcn turtle(hilbert){
const D=10;
ds,dir := T( T(D,0), T(0,-D), T(-D,0), T(0,D) ), 0; // turtle offsets
dx,dy := ds[dir];
img:=PPM(650,650); x,y:=10,10; color:=0x00ff00;
hilbert.replace("A","").replace("B",""); // A & B are no-op during drawing
foreach c in (hilbert){
switch(c){
case("F"){ img.line(x,y, (x+=dx),(y+=dy), color) } // draw forward case("+"){ dir=(dir+1)%4; dx,dy = ds[dir] } // turn right 90* case("-"){ dir=(dir-1)%4; dx,dy = ds[dir] } // turn left 90*
}
}
img.writeJPGFile("hilbert.zkl.jpg");
}</lang> Image at hilbert curve
