Percolation/Site percolation: Difference between revisions
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class Grid { |
class Grid { |
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public: |
public: |
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Grid(int32_t row_count, int32_t col_count, double probability) { |
Grid(const int32_t row_count, const int32_t col_count, const double probability) { |
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create_table(row_count, col_count, probability); |
create_table(row_count, col_count, probability); |
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} |
} |
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} |
} |
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void display() { |
void display() const { |
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for ( uint64_t col = 0; col < table.size(); col++ ) { |
for ( uint64_t col = 0; col < table.size(); col++ ) { |
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for ( uint64_t row = 0; row < table[0].size(); row++ ) { |
for ( uint64_t row = 0; row < table[0].size(); row++ ) { |
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} |
} |
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private: |
private: |
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bool path_exists(int32_t x, int32_t y) { |
bool path_exists(const int32_t x, const int32_t y) { |
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if ( y < 0 || x < 0 || x >= (int32_t) table[0].size() || table[y][x].compare(FILLED) != 0 ) { |
if ( y < 0 || x < 0 || x >= (int32_t) table[0].size() || table[y][x].compare(FILLED) != 0 ) { |
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return false; |
return false; |
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} |
} |
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void create_table(int32_t row_count, int32_t col_count, double probability) { |
void create_table(const int32_t row_count, const int32_t col_count, const double probability) { |
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table.assign(row_count, std::vector<std::string>(col_count, EMPTY)); |
table.assign(row_count, std::vector<std::string>(col_count, EMPTY)); |
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for ( int32_t col = 0; col < row_count; col++ ) { |
for ( int32_t col = 0; col < row_count; col++ ) { |
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Revision as of 21:08, 16 June 2023
You are encouraged to solve this task according to the task description, using any language you may know.
Percolation Simulation
This is a simulation of aspects of mathematical percolation theory.
Mean run density
2D finite grid simulations
Site percolation | Bond percolation | Mean cluster density
Given an rectangular array of cells numbered assume is horizontal and is downwards.
![{\displaystyle \mathrm{cell}[0..M-1, 0..N-1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba727d4b36cd2dc9c727d9c298fca9e8385ba7e)
Assume that the probability of any cell being filled is a constant where
- The task
Simulate creating the array of cells with probability and then testing if there is a route through adjacent filled cells from any on row to any on row , i.e. testing for site percolation.
Given repeat the percolation times to estimate the proportion of times that the fluid can percolate to the bottom for any given .
Show how the probability of percolating through the random grid changes with going from to in increments and with the number of repetitions to estimate the fraction at any given as .
Use an grid of cells for all cases.
Optionally depict a percolation through a cell grid graphically.
Show all output on this page.
11l
UInt32 seed = 0
F nonrandom()
:seed = 1664525 * :seed + 1013904223
R Int(:seed >> 16) / Float(FF'FF)
V (M, nn, t) = (15, 15, 100)
V cell2char = ‘ #abcdefghijklmnopqrstuvwxyz’
V NOT_VISITED = 1
T PercolatedException
(Int, Int) t
F (t)
.t = t
F newgrid(p)
R (0 .< :nn).map(n -> (0 .< :M).map(m -> Int(nonrandom() < @@p)))
F pgrid(cell, percolated)
L(n) 0 .< :nn
print(‘#.) ’.format(n % 10)‘’(0 .< :M).map(m -> :cell2char[@cell[@n][m]]).join(‘ ’))
I percolated != (-1, -1)
V where = percolated[0]
print(‘!) ’(‘ ’ * where)‘’:cell2char[cell[:nn - 1][where]])
F walk_maze(m, n, &cell, indx) -> N
cell[n][m] = indx
I n < :nn - 1 & cell[n + 1][m] == :NOT_VISITED
walk_maze(m, n + 1, &cell, indx)
E I n == :nn - 1
X PercolatedException((m, indx))
I m & cell[n][m - 1] == :NOT_VISITED
walk_maze(m - 1, n, &cell, indx)
I m < :M - 1 & cell[n][m + 1] == :NOT_VISITED
walk_maze(m + 1, n, &cell, indx)
I n & cell[n - 1][m] == :NOT_VISITED
walk_maze(m, n - 1, &cell, indx)
F check_from_top(&cell) -> (Int, Int)?
V (n, walk_index) = (0, 1)
X.try
L(m) 0 .< :M
I cell[n][m] == :NOT_VISITED
walk_index++
walk_maze(m, n, &cell, walk_index)
X.catch PercolatedException ex
R ex.t
R N
V sample_printed = 0B
[Float = Int] pcount
L(p10) 11
V p = p10 / 10.0
pcount[p] = 0
L(tries) 0 .< t
V cell = newgrid(p)
(Int, Int)? percolated = check_from_top(&cell)
I percolated != N
pcount[p]++
I !sample_printed
print("\nSample percolating #. x #., p = #2.2 grid\n".format(M, nn, p))
pgrid(cell, percolated)
sample_printed = 1B
print("\n p: Fraction of #. tries that percolate through\n".format(t))
L(p, c) sorted(pcount.items())
print(‘#.1: #.’.format(p, c / Float(t)))- Output:
Sample percolating 15 x 15, p = 0.50 grid 0) a a a b b b c d # # 1) a a a a b b b d d # # 2) a b b # d # # 3) # # # # d # 4) # # # # # d d d # # # 5) # # # d # # # 6) # # # d # # 7) # # # d d # # # 8) # # d # # # 9) # # d # # # # # 0) # # # d # # # 1) # # # # d d d d # # 2) # # d d # # 3) # # # # # d # # # 4) # # # d # # # # !) d p: Fraction of 100 tries that percolate through 0.0: 0 0.1: 0 0.2: 0 0.3: 0 0.4: 0 0.5: 0.15 0.6: 0.57 0.7: 0.94 0.8: 1 0.9: 1 1.0: 1
C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
char *cell, *start, *end;
int m, n;
void make_grid(int x, int y, double p)
{
int i, j, thresh = p * RAND_MAX;
m = x, n = y;
end = start = realloc(start, (x+1) * (y+1) + 1);
memset(start, 0, m + 1);
cell = end = start + m + 1;
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++)
*end++ = rand() < thresh ? '+' : '.';
*end++ = '\n';
}
end[-1] = 0;
end -= ++m; // end is the first cell of bottom row
}
int ff(char *p) // flood fill
{
if (*p != '+') return 0;
*p = '#';
return p >= end || ff(p+m) || ff(p+1) || ff(p-1) || ff(p-m);
}
int percolate(void)
{
int i;
for (i = 0; i < m && !ff(cell + i); i++);
return i < m;
}
int main(void)
{
make_grid(15, 15, .5);
percolate();
puts("15x15 grid:");
puts(cell);
puts("\nrunning 10,000 tests for each case:");
double p;
int ip, i, cnt;
for (ip = 0; ip <= 10; ip++) {
p = ip / 10.;
for (cnt = i = 0; i < 10000; i++) {
make_grid(15, 15, p);
cnt += percolate();
}
printf("p=%.1f: %.4f\n", p, cnt / 10000.);
}
return 0;
}
- Output:
15x15 grid: .#...##.#.#.#.. ...+.###.####.# ...+..#.+...#.# +..+..##..##### +...+.#....##.. .+..+.##..##.+. ....+.#...##..+ ..+.+.#####.++. +++....#.###.++ .+.+.#.#.##.... ..++.####...++. +.+.+.##..+++.. +..+.+..+.....+ ..........++..+ .+.+.++++.+...+ running 10,000 tests for each case: p=0.0: 0.0000 p=0.1: 0.0000 p=0.2: 0.0000 p=0.3: 0.0000 p=0.4: 0.0032 p=0.5: 0.0902 p=0.6: 0.5771 p=0.7: 0.9587 p=0.8: 0.9996 p=0.9: 1.0000 p=1.0: 1.0000
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#include <stdbool.h>
#define N_COLS 15
#define N_ROWS 15
// Probability granularity 0.0, 0.1, ... 1.0
#define N_STEPS 11
// Simulation tries
#define N_TRIES 100
typedef unsigned char Cell;
enum { EMPTY_CELL = ' ',
FILLED_CELL = '#',
VISITED_CELL = '.' };
typedef Cell Grid[N_ROWS][N_COLS];
void initialize(Grid grid, const double probability) {
for (size_t r = 0; r < N_ROWS; r++)
for (size_t c = 0; c < N_COLS; c++) {
const double rnd = rand() / (double)RAND_MAX;
grid[r][c] = (rnd < probability) ? EMPTY_CELL : FILLED_CELL;
}
}
void show(Grid grid) {
char line[N_COLS + 3];
memset(&line[0], '-', N_COLS + 2);
line[0] = '+';
line[N_COLS + 1] = '+';
line[N_COLS + 2] = '\0';
printf("%s\n", line);
for (size_t r = 0; r < N_ROWS; r++) {
putchar('|');
for (size_t c = 0; c < N_COLS; c++)
putchar(grid[r][c]);
puts("|");
}
printf("%s\n", line);
}
bool walk(Grid grid, const size_t r, const size_t c) {
const size_t bottom = N_ROWS - 1;
grid[r][c] = VISITED_CELL;
if (r < bottom && grid[r + 1][c] == EMPTY_CELL) { // Down.
if (walk(grid, r + 1, c))
return true;
} else if (r == bottom)
return true;
if (c && grid[r][c - 1] == EMPTY_CELL) // Left.
if (walk(grid, r, c - 1))
return true;
if (c < N_COLS - 1 && grid[r][c + 1] == EMPTY_CELL) // Right.
if (walk(grid, r, c + 1))
return true;
if (r && grid[r - 1][c] == EMPTY_CELL) // Up.
if (walk(grid, r - 1, c))
return true;
return false;
}
bool percolate(Grid grid) {
const size_t startR = 0;
for (size_t c = 0; c < N_COLS; c++)
if (grid[startR][c] == EMPTY_CELL)
if (walk(grid, startR, c))
return true;
return false;
}
typedef struct {
double prob;
size_t count;
} Counter;
int main() {
const double probability_step = 1.0 / (N_STEPS - 1);
Counter counters[N_STEPS];
for (size_t i = 0; i < N_STEPS; i++)
counters[i] = (Counter){ i * probability_step, 0 };
bool sample_shown = false;
static Grid grid;
srand(time(NULL));
for (size_t i = 0; i < N_STEPS; i++) {
for (size_t t = 0; t < N_TRIES; t++) {
initialize(grid, counters[i].prob);
if (percolate(grid)) {
counters[i].count++;
if (!sample_shown) {
printf("Percolating sample (%dx%d,"
" probability =%5.2f):\n",
N_COLS, N_ROWS, counters[i].prob);
show(grid);
sample_shown = true;
}
}
}
}
printf("\nFraction of %d tries that percolate through:\n", N_TRIES);
for (size_t i = 0; i < N_STEPS; i++)
printf("%1.1f %1.3f\n", counters[i].prob,
counters[i].count / (double)N_TRIES);
return 0;
}
- Output:
Percolating sample (15x15, probability = 0.40): +---------------+ |###. # # # #| |###.. # ##### | | #. ###### #| |###.... ######| |######. ### # | | #####.###### | |#......... ## | |...#...##.# ## | |##.#...##.### #| | ###..# #. # | |# #######. # ##| | # ##...#### | | ## # .##### | |#######.## ###| |# ## .## # # | +---------------+ Fraction of 100 tries that percolate through: 0.0 0.000 0.1 0.000 0.2 0.000 0.3 0.000 0.4 0.010 0.5 0.070 0.6 0.630 0.7 0.970 0.8 1.000 0.9 1.000 1.0 1.000
C++
#include <iostream>
#include <vector>
#include <string>
#include <random>
#include <iomanip>
std::random_device random;
std::mt19937 generator(random());
std::uniform_real_distribution<double> distribution(0.0F, 1.0F);
class Grid {
public:
Grid(const int32_t row_count, const int32_t col_count, const double probability) {
create_table(row_count, col_count, probability);
}
bool percolate() {
for ( int32_t x = 0; x < (int32_t) table[0].size(); x++ ) {
if ( path_exists(x, 0) ) {
return true;
}
}
return false;
}
void display() const {
for ( uint64_t col = 0; col < table.size(); col++ ) {
for ( uint64_t row = 0; row < table[0].size(); row++ ) {
std::cout << " " << table[col][row];
}
std::cout << std::endl;
}
std::cout << std::endl;
}
private:
bool path_exists(const int32_t x, const int32_t y) {
if ( y < 0 || x < 0 || x >= (int32_t) table[0].size() || table[y][x].compare(FILLED) != 0 ) {
return false;
}
table[y][x] = PATH;
if ( y == (int32_t) table.size() - 1 ) {
return true;
}
return path_exists(x, y + 1) || path_exists(x + 1, y) || path_exists(x - 1, y) || path_exists(x, y - 1);
}
void create_table(const int32_t row_count, const int32_t col_count, const double probability) {
table.assign(row_count, std::vector<std::string>(col_count, EMPTY));
for ( int32_t col = 0; col < row_count; col++ ) {
for ( int32_t row = 0; row < col_count; row++ ) {
table[col][row] = ( distribution(generator) < probability ) ? FILLED: EMPTY;
}
}
}
std::vector<std::vector<std::string>> table;
inline static const std::string EMPTY = " ";
inline static const std::string FILLED = ".";
inline static const std::string PATH = "#";
};
int main() {
const int32_t row_count = 15;
const int32_t col_count = 15;
const int32_t test_count = 1'000;
Grid grid(row_count, col_count, 0.5);
grid.percolate();
grid.display();
std::cout << "Proportion of " << test_count << " tests that percolate through the grid:" << std::endl;
for ( double probable = 0.0; probable <= 1.0; probable += 0.1 ) {
uint32_t percolation_count = 0;
for ( int32_t test = 0; test < test_count; test++) {
Grid test_grid(row_count, col_count, probable);
if ( test_grid.percolate() ) {
percolation_count += 1;
}
}
double percolation_proportion = (double) percolation_count / test_count;
printf("%s%.1f%s%.4f%s", " p = ", probable, ": ", percolation_proportion, "\n");
}
}
- Output:
# . . . . . . . . .
# . . . . . . .
# . . . . . . . . . .
# # . . . . . . .
# . . . . . . . .
# # . . . . .
. # # . . . . .
. . # . . . . . . .
. # # . . . . .
. # . . .
# . . . . . . .
. # # # . . . . .
# # # . . . . .
# # . .
# . . . . . .
Proportion of 1000 tests that percolate through the grid:
p = 0.0: 0.0000
p = 0.1: 0.0000
p = 0.2: 0.0000
p = 0.3: 0.0000
p = 0.4: 0.0020
p = 0.5: 0.0930
p = 0.6: 0.5330
p = 0.7: 0.9750
p = 0.8: 0.9990
p = 0.9: 1.0000
p = 1.0: 1.0000
D
import std.stdio, std.random, std.array, std.datetime;
enum size_t nCols = 15,
nRows = 15,
nSteps = 11, // Probability granularity.
nTries = 20_000; // Simulation tries.
enum Cell : char { empty = ' ', filled = '#', visited = '.' }
alias Grid = Cell[nCols][nRows];
void initialize(ref Grid grid, in double probability, ref Xorshift rng) {
foreach (ref row; grid)
foreach (ref cell; row)
cell = (rng.uniform01 < probability) ? Cell.empty : Cell.filled;
}
void show(in ref Grid grid) @safe {
writefln("%(|%(%c%)|\n%)|", grid);
}
bool percolate(ref Grid grid) pure nothrow @safe @nogc {
bool walk(in size_t r, in size_t c) nothrow @safe @nogc {
enum bottom = nRows - 1;
grid[r][c] = Cell.visited;
if (r < bottom && grid[r + 1][c] == Cell.empty) { // Down.
if (walk(r + 1, c))
return true;
} else if (r == bottom)
return true;
if (c && grid[r][c - 1] == Cell.empty) // Left.
if (walk(r, c - 1))
return true;
if (c < nCols - 1 && grid[r][c + 1] == Cell.empty) // Right.
if (walk(r, c + 1))
return true;
if (r && grid[r - 1][c] == Cell.empty) // Up.
if (walk(r - 1, c))
return true;
return false;
}
enum startR = 0;
foreach (immutable c; 0 .. nCols)
if (grid[startR][c] == Cell.empty)
if (walk(startR, c))
return true;
return false;
}
void main() {
static struct Counter {
double prob;
size_t count;
}
StopWatch sw;
sw.start;
enum probabilityStep = 1.0 / (nSteps - 1);
Counter[nSteps] counters;
foreach (immutable i, ref co; counters)
co.prob = i * probabilityStep;
Grid grid;
bool sampleShown = false;
auto rng = Xorshift(unpredictableSeed);
foreach (ref co; counters) {
foreach (immutable _; 0 .. nTries) {
grid.initialize(co.prob, rng);
if (grid.percolate) {
co.count++;
if (!sampleShown) {
writefln("Percolating sample (%dx%d, probability =%5.2f):",
nCols, nRows, co.prob);
grid.show;
sampleShown = true;
}
}
}
}
sw.stop;
writefln("\nFraction of %d tries that percolate through:", nTries);
foreach (const co; counters)
writefln("%1.3f %1.3f", co.prob, co.count / double(nTries));
writefln("\nSimulations and grid printing performed" ~
" in %3.2f seconds.", sw.peek.msecs / 1000.0);
}
- Output:
Percolating sample (15x15, probability = 0.40): |#.###.##..#. # | |#.###.# ###. #| |#.##..#####. ##| |## #### ...# #| |# # # ##.#..##| |### # ## .#####| | ######.## ##| | ## #..### | |#### ##..##### | |# ###... # | |### ## ##. # | |# ### ##. ### | |## ##### . ####| |# ## # #. ####| |####### #.## ##| Fraction of 20000 tries that percolate through: 0.000 0.000 0.100 0.000 0.200 0.000 0.300 0.000 0.400 0.004 0.500 0.090 0.600 0.565 0.700 0.958 0.800 1.000 0.900 1.000 1.000 1.000 Simulations and grid printing performed in 0.70 seconds.
Factor
USING: arrays combinators combinators.short-circuit formatting
fry generalizations io kernel math math.matrices math.order
math.ranges math.vectors prettyprint random sequences ;
IN: rosetta-code.site-percolation
SYMBOLS: ▓ . v ;
: randomly-filled-matrix ( m n probability -- matrix )
[ random-unit > ▓ . ? ] curry make-matrix ;
: in-bounds? ( matrix loc -- ? )
[ dim { 1 1 } v- ] dip [ 0 rot between? ] 2map [ t = ] all? ;
: set-coord ( obj loc matrix -- ) [ reverse ] dip set-index ;
: get-coord ( matrix loc -- elt ) swap [ first2 ] dip nth nth ;
: (can-percolate?) ( matrix loc -- ? )
{
{ [ 2dup in-bounds? not ] [ 2drop f ] }
{ [ 2dup get-coord { v ▓ } member? ] [ 2drop f ] }
{
[ 2dup second [ dim second 1 - ] dip = ]
[ [ v ] 2dip swap set-coord t ]
}
[
2dup get-coord . =
[ [ v ] 2dip swap [ set-coord ] 2keep swap ] when
{
[ { 1 0 } v+ ] [ { 1 0 } v- ]
[ { 0 1 } v+ ] [ { 0 1 } v- ]
} [ (can-percolate?) ] map-compose 2||
]
} cond ;
: can-percolate? ( matrix -- ? )
dup dim first <iota> [ 0 2array (can-percolate?) ] with find
drop >boolean ;
: show-sample ( -- )
f [ [ can-percolate? ] keep swap ]
[ drop 15 15 0.6 randomly-filled-matrix ] do until
"Sample percolation, p = 0.6" print simple-table. ;
: percolation-rate ( p -- rate )
[ 500 1 ] dip -
'[ 15 15 _ randomly-filled-matrix can-percolate? ] replicate
[ t = ] count 500 / ;
: site-percolation ( -- )
show-sample nl "Running 500 trials at each porosity:" print
10 [1,b] [
10 / dup percolation-rate "p = %.1f: %.3f\n" printf
] each ;
MAIN: site-percolation
- Output:
Sample percolation, p = 0.6 ▓ ▓ v v ▓ . ▓ ▓ ▓ ▓ . ▓ ▓ . ▓ ▓ ▓ v v v ▓ ▓ ▓ ▓ ▓ . . . ▓ ▓ ▓ . v v ▓ . ▓ ▓ ▓ . ▓ . . ▓ ▓ ▓ ▓ . v v ▓ . ▓ . ▓ ▓ ▓ . . ▓ ▓ ▓ . . v v v v ▓ ▓ ▓ ▓ ▓ ▓ ▓ ▓ . ▓ . ▓ ▓ v v ▓ ▓ ▓ . ▓ . . . ▓ . . ▓ v v ▓ . ▓ . . . ▓ . ▓ ▓ . . . v v v ▓ . ▓ . . . ▓ . ▓ ▓ ▓ ▓ v v ▓ . ▓ ▓ ▓ ▓ . . . . ▓ ▓ ▓ v v ▓ . . . . ▓ ▓ ▓ ▓ ▓ ▓ ▓ ▓ v ▓ . ▓ . . ▓ ▓ ▓ . ▓ ▓ . ▓ ▓ v v ▓ . ▓ ▓ ▓ ▓ . . ▓ ▓ ▓ v v v ▓ . ▓ ▓ . ▓ ▓ ▓ . ▓ ▓ ▓ ▓ ▓ v v ▓ . ▓ . ▓ ▓ . . ▓ . . ▓ . ▓ v . . . . ▓ ▓ . ▓ Running 500 trials at each porosity: p = 0.1: 0.000 p = 0.2: 0.000 p = 0.3: 0.000 p = 0.4: 0.002 p = 0.5: 0.074 p = 0.6: 0.508 p = 0.7: 0.970 p = 0.8: 1.000 p = 0.9: 1.000 p = 1.0: 1.000
Fortran
Please see sample compilation and program execution in comments at top of program. Thank you. This example demonstrates recursion and integer constants of a specific kind.
! loosely translated from python.
! compilation: gfortran -Wall -std=f2008 thisfile.f08
!$ a=site && gfortran -o $a -g -O0 -Wall -std=f2008 $a.f08 && $a
!100 trials per
!Fill Fraction goal(%) simulated through paths(%)
! 0 0
! 10 0
! 20 0
! 30 0
! 40 0
! 50 6
!
!
! b b b b h j m m m
! b b b b b h h m m m m m
! b b b h h h m
! b h h h h h h h
! b b h h h h h h h h h
! b b b h h h h h h h h h h
! b b @ h h h h h h h
! @ @ h h h h h h h h
! @ @ @ @ h h h h
! @ @ @ @ h h h h h h
! @ @ @ h h h h h h h
! @ @ @ h h h h h h
! @ h h h h h h
! @ h h h h h h h
! @ @ h h h h h h h h h h
! 60 59
! 70 97
! 80 100
! 90 100
! 100 100
program percolation_site
implicit none
integer, parameter :: m=15,n=15,t=100
!integer, parameter :: m=2,n=2,t=8
integer(kind=1), dimension(m, n) :: grid
real :: p
integer :: i, ip, trial, successes
logical :: success, unseen, q
data unseen/.true./
write(6,'(i3,a11)') t,' trials per'
write(6,'(a21,a30)') 'Fill Fraction goal(%)','simulated through paths(%)'
do ip=0, 10
p = ip/10.0
successes = 0
do trial = 1, t
call newgrid(grid, p)
success = .false.
do i=1, m
q = walk(grid, i) ! deliberately compute all paths
success = success .or. q
end do
if ((ip == 6) .and. unseen) then
call display(grid)
unseen = .false.
end if
successes = successes + merge(1, 0, success)
end do
write(6,'(9x,i3,24x,i3)')ip*10,nint(100*real(successes)/real(t))
end do
contains
logical function walk(grid, start)
integer(kind=1), dimension(m,n), intent(inout) :: grid
integer, intent(in) :: start
walk = rwalk(grid, 1, start, int(start+1,1))
end function walk
recursive function rwalk(grid, i, j, k) result(through)
logical :: through
integer(kind=1), dimension(m,n), intent(inout) :: grid
integer, intent(in) :: i, j
integer(kind=1), intent(in) :: k
logical, dimension(4) :: q
!out of bounds
through = .false.
if (i < 1) return
if (m < i) return
if (j < 1) return
if (n < j) return
!visited or non-pore
if (1_1 /= grid(i, j)) return
!update grid and recurse with neighbors. deny 'shortcircuit' evaluation
grid(i, j) = k
q(1) = rwalk(grid,i+0,j+1,k)
q(2) = rwalk(grid,i+0,j-1,k)
q(3) = rwalk(grid,i+1,j+0,k)
q(4) = rwalk(grid,i-1,j+0,k)
!newly discovered outlet
through = (i == m) .or. any(q)
end function rwalk
subroutine newgrid(grid, probability)
implicit none
real :: probability
integer(kind=1), dimension(m,n), intent(out) :: grid
real, dimension(m,n) :: harvest
call random_number(harvest)
grid = merge(1_1, 0_1, harvest < probability)
end subroutine newgrid
subroutine display(grid)
integer(kind=1), dimension(m,n), intent(in) :: grid
integer :: i, j, k, L
character(len=n*2) :: lineout
write(6,'(/)')
lineout = ' '
do i=1,m
do j=1,n
k = j+j
L = grid(i,j)+1
lineout(k:k) = ' @abcdefghijklmnopqrstuvwxyz'(L:L)
end do
write(6,*) lineout
end do
end subroutine display
end program percolation_site
FreeBASIC
#define SOLID "#"
#define EMPTY " "
#define WET "v"
Dim Shared As String grid()
Dim Shared As Integer last, lastrow, m, n
Sub make_grid(x As Integer, y As Integer, p As Double)
m = x
n = y
Redim Preserve grid(x*(y+1)+1)
last = Len(grid)
Dim As Integer lastrow = last-n
Dim As Integer i, j
For i = 0 To x-1
For j = 1 To y
grid(1+i*(y+1)+j) = Iif(Rnd < p, EMPTY, SOLID)
Next j
Next i
End Sub
Function ff(i As Integer) As Boolean
If i <= 0 Or i >= last Or grid(i) <> EMPTY Then Return 0
grid(i) = WET
Return i >= lastrow Or (ff(i+m+1) Or ff(i+1) Or ff(i-1) Or ff(i-m-1))
End Function
Function percolate() As Integer
For i As Integer = 2 To m+1
If ff(i) Then Return 1
Next i
Return 0
End Function
Dim As Double p
Dim As Integer ip, i, cont
make_grid(15, 15, 0.55)
Print "15x15 grid:"
For i = 1 To Ubound(grid)
Print grid(i);
If i Mod 15 = 0 Then Print
Next i
Print !"\nrunning 10,000 tests for each case:"
For ip As Ubyte = 0 To 10
p = ip / 10
cont = 0
For i = 1 To 10000
make_grid(15, 15, p)
cont += percolate()
Next i
Print Using "p=#.#: #.####"; p; cont/10000
Next ip
SleepGo
package main
import (
"bytes"
"fmt"
"math/rand"
"time"
)
func main() {
const (
m, n = 15, 15
t = 1e4
minp, maxp, Δp = 0, 1, 0.1
)
rand.Seed(2) // Fixed seed for repeatable example grid
g := NewGrid(.5, m, n)
g.Percolate()
fmt.Println(g)
rand.Seed(time.Now().UnixNano()) // could pick a better seed
for p := float64(minp); p < maxp; p += Δp {
count := 0
for i := 0; i < t; i++ {
g := NewGrid(p, m, n)
if g.Percolate() {
count++
}
}
fmt.Printf("p=%.2f, %.4f\n", p, float64(count)/t)
}
}
const (
full = '.'
used = '#'
empty = ' '
)
type grid struct {
cell [][]byte // row first, i.e. [y][x]
}
func NewGrid(p float64, xsize, ysize int) *grid {
g := &grid{cell: make([][]byte, ysize)}
for y := range g.cell {
g.cell[y] = make([]byte, xsize)
for x := range g.cell[y] {
if rand.Float64() < p {
g.cell[y][x] = full
} else {
g.cell[y][x] = empty
}
}
}
return g
}
func (g *grid) String() string {
var buf bytes.Buffer
// Don't really need to call Grow but it helps avoid multiple
// reallocations if the size is large.
buf.Grow((len(g.cell) + 2) * (len(g.cell[0]) + 3))
buf.WriteByte('+')
for _ = range g.cell[0] {
buf.WriteByte('-')
}
buf.WriteString("+\n")
for y := range g.cell {
buf.WriteByte('|')
buf.Write(g.cell[y])
buf.WriteString("|\n")
}
buf.WriteByte('+')
ly := len(g.cell) - 1
for x := range g.cell[ly] {
if g.cell[ly][x] == used {
buf.WriteByte(used)
} else {
buf.WriteByte('-')
}
}
buf.WriteByte('+')
return buf.String()
}
func (g *grid) Percolate() bool {
for x := range g.cell[0] {
if g.use(x, 0) {
return true
}
}
return false
}
func (g *grid) use(x, y int) bool {
if y < 0 || x < 0 || x >= len(g.cell[0]) || g.cell[y][x] != full {
return false // Off the edges, empty, or used
}
g.cell[y][x] = used
if y+1 == len(g.cell) {
return true // We're on the bottom
}
// Try down, right, left, up in that order.
return g.use(x, y+1) ||
g.use(x+1, y) ||
g.use(x-1, y) ||
g.use(x, y-1)
}
- Output:
+---------------+ |#### ###. .. | | ## # # . .| | ### #### .. | |### ##### #.. | | ### # ## .. | |# ## # . ..| |### . #.. . | | ## ##. ..| | ## .. .. # .. | | ## . .#....| |## .. .## . | |# . . . # . | | .. . .#. .. | |. . .... # .. | | . .. . # .. .| +---------#-----+ p=0.00, 0.0000 p=0.10, 0.0000 p=0.20, 0.0000 p=0.30, 0.0000 p=0.40, 0.0040 p=0.50, 0.0980 p=0.60, 0.5641 p=0.70, 0.9583 p=0.80, 0.9995 p=0.90, 1.0000 p=1.00, 1.0000
Haskell
{-# LANGUAGE OverloadedStrings #-}
import Control.Monad
import Control.Monad.Random
import Data.Array.Unboxed
import Data.List
import Formatting
type Field = UArray (Int, Int) Char
-- Start percolating some seepage through a field.
-- Recurse to continue percolation with new seepage.
percolateR :: [(Int, Int)] -> Field -> (Field, [(Int,Int)])
percolateR [] f = (f, [])
percolateR seep f =
let ((xLo,yLo),(xHi,yHi)) = bounds f
validSeep = filter (\p@(x,y) -> x >= xLo
&& x <= xHi
&& y >= yLo
&& y <= yHi
&& f!p == ' ') $ nub $ sort seep
neighbors (x,y) = [(x,y-1), (x,y+1), (x-1,y), (x+1,y)]
in percolateR
(concatMap neighbors validSeep)
(f // map (\p -> (p,'.')) validSeep)
-- Percolate a field. Return the percolated field.
percolate :: Field -> Field
percolate start =
let ((_,_),(xHi,_)) = bounds start
(final, _) = percolateR [(x,0) | x <- [0..xHi]] start
in final
-- Generate a random field.
initField :: Int -> Int -> Double -> Rand StdGen Field
initField w h threshold = do
frnd <- fmap (\rv -> if rv<threshold then ' ' else '#') <$> getRandoms
return $ listArray ((0,0), (w-1, h-1)) frnd
-- Get a list of "leaks" from the bottom of a field.
leaks :: Field -> [Bool]
leaks f =
let ((xLo,_),(xHi,yHi)) = bounds f
in [f!(x,yHi)=='.'| x <- [xLo..xHi]]
-- Run test once; Return bool indicating success or failure.
oneTest :: Int -> Int -> Double -> Rand StdGen Bool
oneTest w h threshold =
or.leaks.percolate <$> initField w h threshold
-- Run test multple times; Return the number of tests that pass.
multiTest :: Int -> Int -> Int -> Double -> Rand StdGen Double
multiTest testCount w h threshold = do
results <- replicateM testCount $ oneTest w h threshold
let leakyCount = length $ filter id results
return $ fromIntegral leakyCount / fromIntegral testCount
-- Display a field with walls and leaks.
showField :: Field -> IO ()
showField a = do
let ((xLo,yLo),(xHi,yHi)) = bounds a
mapM_ print [ [ a!(x,y) | x <- [xLo..xHi]] | y <- [yLo..yHi]]
main :: IO ()
main = do
g <- getStdGen
let w = 15
h = 15
threshold = 0.6
(startField, g2) = runRand (initField w h threshold) g
putStrLn ("Unpercolated field with " ++ show threshold ++ " threshold.")
putStrLn ""
showField startField
putStrLn ""
putStrLn "Same field after percolation."
putStrLn ""
showField $ percolate startField
let testCount = 10000
densityCount = 10
putStrLn ""
putStrLn ( "Results of running percolation test " ++ show testCount
++ " times with thresholds ranging from 0/" ++ show densityCount
++ " to " ++ show densityCount ++ "/" ++ show densityCount ++ " .")
let densities = [0..densityCount]
tests = sequence [multiTest testCount w h v
| density <- densities,
let v = fromIntegral density / fromIntegral densityCount ]
results = zip densities (evalRand tests g2)
mapM_ print [format ("p=" % int % "/" % int % " -> " % fixed 4) density densityCount x | (density,x) <- results]
- Output:
Unpercolated field with 0.6 threshold. " ### # # # ## " "### # ## # # " " ##### # ##" "# # ## # " "### # " " ### ### # " " ### # ### ##" " # ## # ##" " # # # # ##" "### ## # " " ## # ##" " # # ## ## #" " ### ## ## " "#### # # ## ##" " # # # " Same field after percolation. "..###.#.#.#.##." "### #.##..#.#.." "..#####..#...##" "#....#.##..#..." "###.........#.." " ###.###.#....." " ### #..###.##" " # ##.#....##" " # #...#.#..##" "### ##.#......." " ## #......##" " # #.##.##.#" " ### ##..##...." "#### # #..##.##" " # #....# " Results of running percolation test 10000 times with thresholds ranging from 0/10 to 10/10 . "p=0/10 -> 0.0000" "p=1/10 -> 0.0000" "p=2/10 -> 0.0000" "p=3/10 -> 0.0000" "p=4/10 -> 0.0028" "p=5/10 -> 0.0910" "p=6/10 -> 0.5684" "p=7/10 -> 0.9572" "p=8/10 -> 0.9997" "p=9/10 -> 1.0000" "p=10/10 -> 1.0000"
J
One approach:
groups=:[: +/\ 2 </\ 0 , *
ooze=: [ >. [ +&* [ * [: ; groups@[ <@(* * 2 < >./)/. +
percolate=: ooze/\.@|.^:2^:_@(* (1 + # {. 1:))
trial=: percolate@([ >: ]?@$0:)
simulate=: %@[ * [: +/ (2 e. {:)@trial&15 15"0@#
Example Statistics:
,.' P THRU';(, 100&simulate)"0 (i.%<:)11
┌────────┐
│ P THRU│
├────────┤
│ 0 0│
│0.1 0│
│0.2 0│
│0.3 0│
│0.4 0.01│
│0.5 0.09│
│0.6 0.61│
│0.7 0.97│
│0.8 1│
│0.9 1│
│ 1 1│
└────────┘
Worked sample:
1j1 #"1 ' .#'{~ percolate 0.6>:?15 15$0
# # # # # # # #
# # # # # # # # # # # #
# # # # # # # #
# # # # # # # # #
# . # # # # # #
# # # # # # # # # #
# # # # # # # # # # # # #
# # # # # # # # # #
. # #
. . # # # #
. . . . # # # # # # # # #
. . . . # # # # # # #
. . . # . # # #
. . . . . . . # # .
. . . . . . . . # #
An explanation with examples would be somewhat longer than the implementation.
Alternative implementation (with an incompatible internal API):
any =: +./
all =: *./
quickCheck =: [: all [: (any"1) 2 *./\ ] NB. a complete path requires connections between all row pairs
percolate =: 15 15&$: : (dyad define) NB. returns 0 iff blocked Use: (N, M) percolate P
NB. make a binary grid
GRID =: y (> ?@($&0)) x
NB. compute the return value
if. -. quickCheck GRID do. 0 return. end.
STARTING_SITES =. 0 ,. ({. GRID) # i. {: x NB. indexes of 1 in head row of GRID
any STARTING_SITES check GRID
)
NB. use local copy of GRID. Too slow.
check =: dyad define"1 2 NB. return 1 iff through path found use: START check GRID
GRID =. y
LOCATION =. x
if. 0 (= #) LOCATION do. 0 return. end. NB. no starting point? 0
if. LOCATION any@:((>: , 0 > [) $) GRID do. 0 return. end. NB. off grid? 0
INDEX =. <LOCATION
if. 1 ~: INDEX { GRID do. 0 return. end. NB. fail. either already looked here or non-path
if. (>: {. LOCATION) = (# GRID) do. 1 return. end. NB. Success! (display GRID here)
G =: GRID =. INDEX (>:@:{)`[`]}GRID
any GRID check~ LOCATION +"1 (, -)0 1,:1 0
)
NB. use global GRID.
check =: dyad define"1 2 NB. return 1 iff through path found use: START check GRID
LOCATION =. x
if. 0 (= #) LOCATION do. 0 return. end. NB. no starting point? 0
if. LOCATION any@:((>: , 0 > [) $) GRID do. 0 return. end. NB. off grid? 0
INDEX =. <LOCATION
if. 1 ~: INDEX { GRID do. 0 return. end. NB. fail. either already looked here or non-path
if. (>: {. LOCATION) = (# GRID) do. 1 return. end. NB. Success! (display GRID here)
GRID =: INDEX (>:@:{)`[`]}GRID
any GRID check~ LOCATION +"1 (, -)0 1,:1 0
)
simulate =: 100&$: : ([ %~ [: +/ [: percolate"0 #) NB. return fraction of connected cases. Use: T simulate P
,. ' P THRU' ; (, 100x&simulate)"0 (i. % <:)11x
+-----------+
| P THRU |
+-----------+
| 0 0|
|1r10 0|
| 1r5 0|
|3r10 0|
| 2r5 1r100|
| 1r2 1r20|
| 3r5 31r50|
|7r10 97r100|
| 4r5 1|
|9r10 1|
| 1 1|
+-----------+
NB. example
simulate 0.6
0.51
GRID NB. the final grid of the 100 simulated cases.
2 2 2 2 0 2 2 2 2 0 2 2 0 0 2
2 0 0 2 0 0 2 0 2 0 2 0 0 1 0
2 0 1 0 2 2 0 2 2 0 2 2 0 1 0
2 2 0 0 0 2 2 0 2 0 2 0 0 0 1
0 2 2 2 2 2 2 0 2 0 2 0 0 1 1
0 2 0 2 0 0 0 0 0 0 0 1 1 0 1
0 0 0 0 1 0 0 1 1 1 0 1 1 0 1
1 1 1 1 1 1 1 0 0 0 1 1 0 1 1
0 0 1 1 1 0 1 1 0 0 1 1 1 0 1
0 1 0 1 1 1 1 1 0 0 1 1 1 1 1
1 1 1 1 0 1 1 0 1 1 0 0 1 1 1
0 1 1 1 0 1 1 0 0 0 1 1 1 1 1
0 0 0 0 1 0 1 1 1 1 1 0 0 1 0
1 1 1 1 0 1 1 1 1 1 0 1 0 0 0
1 0 1 1 1 1 1 0 0 1 1 1 1 1 1
(0 ,. 0 6 10 14) check GRID NB. show possible starting points all fail
0 0 0 0
1j1#"1 GRID { '#',~u: 32 16bb7 NB. sample paths with unicode pepper.
# # # # # # # # # # #
# # # # # ·
# · # # # # # # ·
# # # # # # ·
# # # # # # # # · ·
# # · · ·
· · · · · · ·
· · · · · · · · · · ·
· · · · · · · · ·
· · · · · · · · · · ·
· · · · · · · · · · ·
· · · · · · · · · ·
· · · · · · ·
· · · · · · · · · ·
· · · · · · · · · · · ·
Java
import java.util.concurrent.ThreadLocalRandom;
public final class PercolationSite {
public static void main(String[] aArgs) {
final int rowCount = 15;
final int colCount = 15;
final int testCount = 1_000;
Grid grid = new Grid(rowCount, colCount, 0.5);
grid.percolate();
grid.display();
System.out.println("Proportion of " + testCount + " tests that percolate through the grid:");
for ( double probable = 0.0; probable <= 1.0; probable += 0.1 ) {
int percolationCount = 0;
for ( int test = 0; test < testCount; test++) {
Grid testGrid = new Grid(rowCount, colCount, probable);
if ( testGrid.percolate() ) {
percolationCount += 1;
}
}
double percolationProportion = (double) percolationCount / testCount;
System.out.println(String.format("%s%.1f%s%.4f", " p = ", probable, ": ", percolationProportion));
}
}
}
final class Grid {
public Grid(int aRowCount, int aColCount, double aProbability) {
createGrid(aRowCount, aColCount, aProbability);
}
public boolean percolate() {
for ( int x = 0; x < table[0].length; x++ ) {
if ( pathExists(x, 0) ) {
return true;
}
}
return false;
}
public void display() {
for ( int col = 0; col < table.length; col++ ) {
for ( int row = 0; row < table[0].length; row++ ) {
System.out.print(" " + table[col][row]);
}
System.out.println();
}
System.out.println();
}
private boolean pathExists(int aX, int aY) {
if ( aY < 0 || aX < 0 || aX >= table[0].length || table[aY][aX].compareTo(FILLED) != 0 ) {
return false;
}
table[aY][aX] = PATH;
if ( aY == table.length - 1 ) {
return true;
}
return pathExists(aX, aY + 1) || pathExists(aX + 1, aY) || pathExists(aX - 1, aY) || pathExists(aX, aY - 1);
}
private void createGrid(int aRowCount, int aColCount, double aProbability) {
table = new String[aRowCount][aColCount];
for ( int col = 0; col < aRowCount; col++ ) {
for ( int row = 0; row < aColCount; row++ ) {
table[col][row] = ( RANDOM.nextFloat(1.0F) < aProbability ) ? FILLED: EMPTY;
}
}
}
private String[][] table;
private static final String EMPTY = " ";
private static final String FILLED = ".";
private static final String PATH = "#";
private static final ThreadLocalRandom RANDOM = ThreadLocalRandom.current();
}
- Output:
# . .
. . # # . .
. . . # # . . . . .
. . . # # # . . . .
. . # # . . .
. . . # # . . . . .
. . # # # # . . . .
. . # . . . . .
. . . # # . . . . . .
. # . . . .
. . # . . . .
. # # . . . . .
# . . . . . .
. . # . . . . . . .
. . # . . . . . . .
Proportion of 1000 tests that percolate through the grid:
p = 0.0: 0.0000
p = 0.1: 0.0000
p = 0.2: 0.0000
p = 0.3: 0.0000
p = 0.4: 0.0060
p = 0.5: 0.1040
p = 0.6: 0.5670
p = 0.7: 0.9480
p = 0.8: 1.0000
p = 0.9: 1.0000
p = 1.0: 1.0000
Julia
using Printf, Distributions
newgrid(p::Float64, M::Int=15, N::Int=15) = rand(Bernoulli(p), M, N)
function walkmaze!(grid::Matrix{Int}, r::Int, c::Int, indx::Int)
NOT_VISITED = 1 # const
N, M = size(grid)
dirs = [[1, 0], [-1, 0], [0, 1], [1, 0]]
# fill cell
grid[r, c] = indx
# is the bottom line?
rst = r == N
# for each direction, if has not reached the bottom yet and can continue go to that direction
for d in dirs
rr, cc = (r, c) .+ d
if !rst && checkbounds(Bool, grid, rr, cc) && grid[rr, cc] == NOT_VISITED
rst = walkmaze!(grid, rr, cc, indx)
end
end
return rst
end
function checkpath!(grid::Matrix{Int})
NOT_VISITED = 1 # const
N, M = size(grid)
walkind = 1
for m in 1:M
if grid[1, m] == NOT_VISITED
walkind += 1
if walkmaze!(grid, 1, m, walkind)
return true
end
end
end
return false
end
function printgrid(G::Matrix{Int})
LETTERS = vcat(' ', '#', 'A':'Z')
for r in 1:size(G, 1)
println(r % 10, ") ", join(LETTERS[G[r, :] .+ 1], ' '))
end
if any(G[end, :] .> 1)
println("!) ", join((ifelse(c > 1, LETTERS[c+1], ' ') for c in G[end, :]), ' '))
end
end
const nrep = 1000 # const
sampleprinted = false
p = collect(0.0:0.1:1.0)
f = similar(p)
for i in linearindices(f)
c = 0
for _ in 1:nrep
G = newgrid(p[i])
perc = checkpath!(G)
if perc
c += 1
if !sampleprinted
@printf("Sample percolation, %i×%i grid, p = %.2f\n\n", size(G, 1), size(G, 2), p[i])
printgrid(G)
sampleprinted = true
end
end
end
f[i] = c / nrep
end
println("\nFrequencies for $nrep tries that percolate through\n")
for (pi, fi) in zip(p, f)
@printf("p = %.1f ⇛ f = %.3f\n", pi, fi)
end
- Output:
Sample percolation, 15×15 grid, p = 0.40 1) A A B # # # # # 2) A A B # # # # 3) A B B B # # 4) # B B # # # 5) # # B B B # # # 6) # # # B B # # 7) B # # # 8) # B # # 9) # B B 0) # # B # # # # 1) # # B 2) # # # B # # # 3) # # # # B # 4) # # # B B # # # 5) # # B # # # !) B Frequencies for 1000 tries that percolate through p = 0.0 ⇛ f = 0.000 p = 0.1 ⇛ f = 0.000 p = 0.2 ⇛ f = 0.000 p = 0.3 ⇛ f = 0.000 p = 0.4 ⇛ f = 0.001 p = 0.5 ⇛ f = 0.089 p = 0.6 ⇛ f = 0.559 p = 0.7 ⇛ f = 0.956 p = 0.8 ⇛ f = 1.000 p = 0.9 ⇛ f = 1.000 p = 1.0 ⇛ f = 1.000
Kotlin
// version 1.2.10
import java.util.Random
val rand = Random()
const val RAND_MAX = 32767
const val NUL = '\u0000'
val x = 15
val y = 15
var grid = StringBuilder((x + 1) * (y + 1) + 1)
var cell = 0
var end = 0
var m = 0
var n = 0
fun makeGrid(p: Double) {
val thresh = (p * RAND_MAX).toInt()
m = x
n = y
grid.setLength(0) // clears grid
grid.setLength(m + 1) // sets first (m + 1) chars to NUL
end = m + 1
cell = m + 1
for (i in 0 until n) {
for (j in 0 until m) {
val r = rand.nextInt(RAND_MAX + 1)
grid.append(if (r < thresh) '+' else '.')
end++
}
grid.append('\n')
end++
}
grid[end - 1] = NUL
end -= ++m // end is the index of the first cell of bottom row
}
fun ff(p: Int): Boolean { // flood fill
if (grid[p] != '+') return false
grid[p] = '#'
return p >= end || ff(p + m) || ff(p + 1) || ff(p - 1) || ff(p - m)
}
fun percolate(): Boolean {
var i = 0
while (i < m && !ff(cell + i)) i++
return i < m
}
fun main(args: Array<String>) {
makeGrid(0.5)
percolate()
println("$x x $y grid:")
println(grid)
println("\nrunning 10,000 tests for each case:")
for (ip in 0..10) {
val p = ip / 10.0
var cnt = 0
for (i in 0 until 10_000) {
makeGrid(p)
if (percolate()) cnt++
}
println("p = %.1f: %.4f".format(p, cnt / 10000.0))
}
}
Sample output:
15 x 15 grid: .#.##..##..##.# .#.##..#..###.# .....++.###.#.. ....+.+..###... +.+.+..+...#### ..+.+.+..#..##. ++...+..###.### +++.+.+.#.###.# +..++...#.#.### ++..+.+.#..+... .+.+.+++..+.+++ ...++.+.++++... +..+..+.++.++.+ +...++..++...+. ..+.+++..+..++. running 10,000 tests for each case: p = 0.0: 0.0000 p = 0.1: 0.0000 p = 0.2: 0.0000 p = 0.3: 0.0000 p = 0.4: 0.0038 p = 0.5: 0.0998 p = 0.6: 0.5617 p = 0.7: 0.9558 p = 0.8: 0.9998 p = 0.9: 1.0000 p = 1.0: 1.0000
Nim
import random, sequtils, strformat, strutils
type Grid = seq[string] # Row first, i.e. [y][x].
const
Full = '.'
Used = '#'
Empty = ' '
proc newGrid(p: float; xsize, ysize: Positive): Grid =
result = newSeqWith(ysize, newString(xsize))
for row in result.mitems:
for cell in row.mitems:
cell = if rand(1.0) < p: Full else: Empty
proc `$`(grid: Grid): string =
# Preallocate result to avoid multiple reallocations.
result = newStringOfCap((grid.len + 2) * (grid[0].len + 3))
result.add '+'
result.add repeat('-', grid[0].len)
result.add "+\n"
for row in grid:
result.add '|'
result.add row
result.add "|\n"
result.add '+'
for cell in grid[^1]:
result.add if cell == Used: Used else: '-'
result.add '+'
proc use(grid: var Grid; x, y: int): bool =
if y < 0 or x < 0 or x >= grid[0].len or grid[y][x] != Full:
return false # Off the edges, empty, or used.
grid[y][x] = Used
if y == grid.high: return true # On the bottom.
# Try down, right, left, up in that order.
result = grid.use(x, y + 1) or grid.use(x + 1, y) or
grid.use(x - 1, y) or grid.use(x, y - 1)
proc percolate(grid: var Grid): bool =
for x in 0..grid[0].high:
if grid.use(x, 0): return true
const
M = 15
N = 15
T = 1000
MinP = 0.0
MaxP = 1.0
ΔP = 0.1
randomize()
var grid = newGrid(0.5, M, N)
discard grid.percolate()
echo grid
echo ""
var p = MinP
while p < MaxP:
var count = 0
for _ in 1..T:
var grid = newGrid(p, M, N)
if grid.percolate(): inc count
echo &"p = {p:.2f}: {count / T:.4f}"
p += ΔP
- Output:
+---------------+ |# # ### . .| | ### #. . ...| | # .##### . | | ## # .. | | ... . #... | |.. . . ### | | . .# . ..| |.. .. #### | | . . .# .. | | . . ## . | |. . .. #. ..| |. .. ..# . . | | .. . .# | | ... .# .. | | .. . # .. . | +--------#------+ p = 0.00: 0.0000 p = 0.10: 0.0000 p = 0.20: 0.0000 p = 0.30: 0.0000 p = 0.40: 0.0020 p = 0.50: 0.1070 p = 0.60: 0.5620 p = 0.70: 0.9590 p = 0.80: 1.0000 p = 0.90: 1.0000 p = 1.00: 1.0000
Perl
my $block = '▒';
my $water = '+';
my $pore = ' ';
my $grid = 15;
my @site;
$D{$_} = $i++ for qw<DeadEnd Up Right Down Left>;
sub deq { defined $_[0] && $_[0] eq $_[1] }
sub percolate {
my($prob) = shift || 0.6;
$site[0] = [($pore) x $grid];
for my $y (1..$grid) {
for my $x (0..$grid-1) {
$site[$y][$x] = rand() < $prob ? $pore : $block;
}
}
$site[$grid + 1] = [($pore) x $grid];
$site[0][0] = $water;
my $x = 0;
my $y = 0;
my @stack;
while () {
if (my $dir = direction($x,$y)) {
push @stack, [$x,$y];
($x,$y) = move($dir, $x, $y)
} else {
return 0 unless @stack;
($x,$y) = @{pop @stack}
}
return 1 if $y > $grid;
}
}
sub direction {
my($x, $y) = @_;
return $D{Down} if deq($site[$y+1][$x ], $pore);
return $D{Right} if deq($site[$y ][$x+1], $pore);
return $D{Left} if deq($site[$y ][$x-1], $pore);
return $D{Up} if deq($site[$y-1][$x ], $pore);
return $D{DeadEnd};
}
sub move {
my($dir,$x,$y) = @_;
$site[--$y][ $x] = $water if $dir == $D{Up};
$site[++$y][ $x] = $water if $dir == $D{Down};
$site[ $y][ --$x] = $water if $dir == $D{Left};
$site[ $y][ ++$x] = $water if $dir == $D{Right};
$x, $y
}
my $prob = 0.65;
percolate($prob);
print "Sample percolation at $prob\n";
print join '', @$_, "\n" for @site;
print "\n";
my $tests = 100;
print "Doing $tests trials at each porosity:\n";
my @table;
for my $p (1 .. 10) {
$p = $p/10;
my $total = 0;
$total += percolate($p) for 1..$tests;
push @table, sprintf "p = %0.1f: %0.2f", $p, $total / $tests
}
print "$_\n" for @table;
- Output:
Sample percolation at 0.65
+++
▒▒+ ▒ ▒
▒+▒▒▒ ▒▒ ▒▒ ▒
+ ▒▒▒▒▒▒
▒▒++▒ ▒▒ ▒
▒ ▒++ ▒ ▒
▒▒▒+++▒ ▒ ▒
▒ ▒▒+▒ ▒ ▒
▒ ▒+ ▒
▒ ▒++▒▒
▒ ▒+ ▒ ▒
▒▒ ▒ ++ ▒
▒ ▒▒▒▒▒++ ▒
▒ ▒ ▒ ▒▒+ ▒
▒ ▒▒▒ + ▒▒
▒ ▒ + ▒▒
+
Doing 100 trials at each porosity:
p = 0.1: 0.00
p = 0.2: 0.00
p = 0.3: 0.00
p = 0.4: 0.01
p = 0.5: 0.10
p = 0.6: 0.51
p = 0.7: 0.89
p = 0.8: 1.00
p = 0.9: 1.00
p = 1.0: 1.00
Phix
with javascript_semantics string grid integer m, n, last, lastrow enum SOLID = '#', EMPTY=' ', WET = 'v' procedure make_grid(integer x, y, atom p) m = x n = y grid = repeat('\n',x*(y+1)+1) last = length(grid) lastrow = last-n for i=0 to x-1 do for j=1 to y do grid[1+i*(y+1)+j] = iff(rnd()<p?EMPTY:SOLID) end for end for end procedure function ff(integer i) -- flood_fill if i<=0 or i>=last or grid[i]!=EMPTY then return 0 end if grid[i] = WET return i>=lastrow or ff(i+m+1) or ff(i+1) or ff(i-1) or ff(i-m-1) end function function percolate() for i=2 to m+1 do if ff(i) then return true end if end for return false end function procedure main() make_grid(15,15,0.55) {} = percolate() printf(1,"%dx%d grid:%s",{15,15,grid}) puts(1,"\nrunning 10,000 tests for each case:\n") for ip=0 to 10 do atom p = ip/10 integer count = 0 for i=1 to 10000 do make_grid(15, 15, p) count += percolate() end for printf(1,"p=%.1f: %6.4f\n", {p, count/10000}) end for end procedure main()
- Output:
15x15 grid:
#v###vvv###vv#
##vvv##v# #v #
#vvvvvv# v #
##vvv#vv# ##vv#
#vv##### # #vv
### # ### ###v
# ##### ##vv
### # # #vvvv
### #### ##vvv
## ## vvvvvv
# #v##vvv
## #vv# ##v
# v######
v
##### v#### #
running 10,000 tests for each case:
p=0.0: 0.0000
p=0.1: 0.0000
p=0.2: 0.0000
p=0.3: 0.0000
p=0.4: 0.0035
p=0.5: 0.0933
p=0.6: 0.5601
p=0.7: 0.9561
p=0.8: 0.9997
p=0.9: 1.0000
p=1.0: 1.0000
Python
from random import random
import string
from pprint import pprint as pp
M, N, t = 15, 15, 100
cell2char = ' #' + string.ascii_letters
NOT_VISITED = 1 # filled cell not walked
class PercolatedException(Exception): pass
def newgrid(p):
return [[int(random() < p) for m in range(M)] for n in range(N)] # cell
def pgrid(cell, percolated=None):
for n in range(N):
print( '%i) ' % (n % 10)
+ ' '.join(cell2char[cell[n][m]] for m in range(M)))
if percolated:
where = percolated.args[0][0]
print('!) ' + ' ' * where + cell2char[cell[n][where]])
def check_from_top(cell):
n, walk_index = 0, 1
try:
for m in range(M):
if cell[n][m] == NOT_VISITED:
walk_index += 1
walk_maze(m, n, cell, walk_index)
except PercolatedException as ex:
return ex
return None
def walk_maze(m, n, cell, indx):
# fill cell
cell[n][m] = indx
# down
if n < N - 1 and cell[n+1][m] == NOT_VISITED:
walk_maze(m, n+1, cell, indx)
# THE bottom
elif n == N - 1:
raise PercolatedException((m, indx))
# left
if m and cell[n][m - 1] == NOT_VISITED:
walk_maze(m-1, n, cell, indx)
# right
if m < M - 1 and cell[n][m + 1] == NOT_VISITED:
walk_maze(m+1, n, cell, indx)
# up
if n and cell[n-1][m] == NOT_VISITED:
walk_maze(m, n-1, cell, indx)
if __name__ == '__main__':
sample_printed = False
pcount = {}
for p10 in range(11):
p = p10 / 10.0
pcount[p] = 0
for tries in range(t):
cell = newgrid(p)
percolated = check_from_top(cell)
if percolated:
pcount[p] += 1
if not sample_printed:
print('\nSample percolating %i x %i, p = %5.2f grid\n' % (M, N, p))
pgrid(cell, percolated)
sample_printed = True
print('\n p: Fraction of %i tries that percolate through\n' % t )
pp({p:c/float(t) for p, c in pcount.items()})
- Output:
The Ascii art grid of cells has blanks for cells that were not filled. Filled cells start off as the '#', hash character and are changed to a succession of printable characters by successive tries to navigate from the top, (top - left actually), filled cell to the bottom.
The '!)' row shows where the percolation finished and you can follow the letter backwards from that row, (letter 'c' in this case), to get the route. The program stops after finding its first route through.
Sample percolating 15 x 15, p = 0.40 grid
0) a a a b c #
1) a a # c c # #
2) # # # # c # # #
3) # # # # # c
4) # # c c c c c c
5) # # # # # # c c c
6) # # # c c c
7) # # # # # # # c
8) # # # # # c c c
9) # # # c
0) # # # # # # c c # #
1) # # # # c
2) # # # # # # c c c c
3) # # # # c c c c
4) # # c #
!) c
p: Fraction of 100 tries that percolate through
{0.0: 0.0,
0.1: 0.0,
0.2: 0.0,
0.3: 0.0,
0.4: 0.01,
0.5: 0.11,
0.6: 0.59,
0.7: 0.94,
0.8: 1.0,
0.9: 1.0,
1.0: 1.0}
Note the abrupt change in percolation at around p = 0.6. These abrupt changes are expected.
Racket
#lang racket
(require racket/require (only-in racket/fixnum for*/fxvector))
(require (filtered-in (lambda (name) (regexp-replace #rx"unsafe-" name ""))
racket/unsafe/ops))
(define cell-empty 0)
(define cell-filled 1)
(define cell-wall 2)
(define cell-visited 3)
(define cell-exit 4)
(define ((percol->generator p)) (if (< (random) p) cell-filled cell-empty))
(define t (make-parameter 1000))
(define ((make-percol-grid M N) p)
(define p->10 (percol->generator p))
(define M+1 (fx+ 1 M))
(define M+2 (fx+ 2 M))
(for*/fxvector
#:length (fx* N M+2)
((n (in-range N)) (m (in-range M+2)))
(cond
[(fx= 0 m) cell-wall]
[(fx= m M+1) cell-wall]
[else (p->10)])))
(define (cell->str c) (substring " #|+*" c (fx+ 1 c)))
(define ((draw-percol-grid M N) g)
(define M+2 (fx+ M 2))
(for ((row N))
(for ((col (in-range M+2)))
(define idx (fx+ (fx* M+2 row) col))
(printf "~a" (cell->str (fxvector-ref g idx))))
(newline)))
(define ((percolate-percol-grid?! M N) g)
(define M+2 (fx+ M 2))
(define N-1 (fx- N 1))
(define max-idx (fx* N M+2))
(define (inner-percolate g idx)
(define row (fxquotient idx M+2))
(cond
((fx< idx 0) #f)
((fx>= idx max-idx) #f)
((fx= N-1 row) (fxvector-set! g idx cell-exit) #t)
((fx= cell-filled (fxvector-ref g idx))
(fxvector-set! g idx cell-visited)
(or
; gravity first (thanks Mr Newton)
(inner-percolate g (fx+ idx M+2))
; stick-to-the-left
(inner-percolate g (fx- idx 1))
(inner-percolate g (fx+ idx 1))
; go uphill only if we have to!
(inner-percolate g (fx- idx M+2))))
(else #f)))
(for/first ((m (in-range 1 M+2)) #:when (inner-percolate g m)) g))
(define make-15x15-grid (make-percol-grid 15 15))
(define draw-15x15-grid (draw-percol-grid 15 15))
(define perc-15x15-grid?! (percolate-percol-grid?! 15 15))
(define (display-sample-percolation p)
(printf "Percolation sample: p=~a~%" p)
(for*/first
((i (in-naturals))
(g (in-value (make-15x15-grid 0.6)))
#:when (perc-15x15-grid?! g))
(draw-15x15-grid g))
(newline))
(display-sample-percolation 0.4)
(for ((p (sequence-map (curry * 1/10) (in-range 0 (add1 10)))))
(define n-percolated-grids
(for/sum
((i (in-range (t))) #:when (perc-15x15-grid?! (make-15x15-grid p))) 1))
(define proportion-percolated (/ n-percolated-grids (t)))
(printf "p=~a\t->\t~a~%" p (real->decimal-string proportion-percolated 4)))
- Output:
Percolation sample: p=0.4 |+++ ++++ + +++| | +++ ++ # +| | + ++ ##++| | ## + ###+ | | ###### + #+++#| | ##### + + #| |## # # +++++## | |### # ++ +++# | |## ## +++++# | |# ### ++ + #| | ## ## +++ ##| |## ## +++ # #| |### # +### | |#### ####+ # | |# ## # *# #| p=0 -> 0.0000 p=1/10 -> 0.0000 p=1/5 -> 0.0000 p=3/10 -> 0.0000 p=2/5 -> 0.0030 p=1/2 -> 0.1110 p=3/5 -> 0.5830 p=7/10 -> 0.9530 p=4/5 -> 1.0000 p=9/10 -> 1.0000 p=1 -> 1.0000
Raku
(formerly Perl 6)
my $block = '▒';
my $water = '+';
my $pore = ' ';
my $grid = 15;
my @site;
enum Direction <DeadEnd Up Right Down Left>;
say 'Sample percolation at .6';
percolate(.6);
.join.say for @site;
say "\n";
my $tests = 1000;
say "Doing $tests trials at each porosity:";
for .1, .2 ... 1 -> $p {
printf "p = %0.1f: %0.3f\n", $p, (sum percolate($p) xx $tests) / $tests
}
sub infix:<deq> ( $a, $b ) { $a.defined && ($a eq $b) }
sub percolate ( $prob = .6 ) {
@site[0] = [$pore xx $grid];
@site[$grid + 1] = [$pore xx $grid];
for ^$grid X 1..$grid -> ($x, $y) {
@site[$y;$x] = rand < $prob ?? $pore !! $block
}
@site[0;0] = $water;
my @stack;
my $current = [0;0];
loop {
if my $dir = direction( $current ) {
@stack.push: $current;
$current = move( $dir, $current )
}
else {
return False unless @stack;
$current = @stack.pop
}
return True if $current[1] > $grid
}
sub direction( [$x, $y] ) {
(Down if @site[$y + 1][$x] deq $pore) ||
(Left if @site[$y][$x - 1] deq $pore) ||
(Right if @site[$y][$x + 1] deq $pore) ||
(Up if @site[$y - 1][$x] deq $pore) ||
DeadEnd
}
sub move ( $dir, @cur ) {
my ( $x, $y ) = @cur;
given $dir {
when Up { @site[--$y][$x] = $water }
when Down { @site[++$y][$x] = $water }
when Left { @site[$y][--$x] = $water }
when Right { @site[$y][++$x] = $water }
}
[$x, $y]
}
}
- Output:
Sample percolation at .6
++++
▒▒▒+ ▒ ▒ ▒ ▒ ▒▒
▒▒++ ▒▒ ▒▒
▒+ ▒▒ ▒ ▒▒
▒▒ ▒++++▒ ▒▒
▒ ▒+▒▒+▒ ▒
▒++▒++ ▒▒▒ ▒
▒▒▒ +▒
▒▒ ▒ ▒++ ▒ ▒▒
▒▒▒▒▒▒▒+▒▒▒
▒ ▒ + ▒
▒▒ ▒+ ▒ ▒ ▒
▒ ▒ ▒▒+ ▒
▒▒ ▒ ▒++▒ ▒
▒ +▒ ▒▒ ▒▒
▒ ▒▒▒+ ▒▒ ▒
+
Doing 1000 trials at each porosity:
p = 0.1: 0.000
p = 0.2: 0.000
p = 0.3: 0.000
p = 0.4: 0.005
p = 0.5: 0.096
p = 0.6: 0.573
p = 0.7: 0.959
p = 0.8: 0.999
p = 0.9: 1.000
p = 1.0: 1.000
Sidef
class Percolate {
has block = '▒'
has water = '+'
has pore = ' '
has grid = 15
has site = []
enum <DeadEnd, Up, Right, Down, Left>
method direction(x, y) {
((site[y + 1][x] == pore) && Down ) ||
((site[y][x - 1] == pore) && Left ) ||
((site[y][x + 1] == pore) && Right) ||
((site[y - 1][x] == pore) && Up ) ||
DeadEnd
}
method move(dir, x, y) {
given (dir) {
when (Up) { site[--y][x] = water }
when (Down) { site[++y][x] = water }
when (Left) { site[y][--x] = water }
when (Right) { site[y][++x] = water }
}
return (x, y)
}
method percolate (prob = 0.6) {
site[0] = grid.of(pore)
site[grid + 1] = grid.of(pore)
for x = ^grid, y = 1..grid {
site[y][x] = (1.rand < prob ? pore : block)
}
site[0][0] = water
var stack = []
var (x, y) = (0, 0)
loop {
if (var dir = self.direction(x, y)) {
stack << [x, y]
(x,y) = self.move(dir, x, y)
}
else {
stack || return 0
(x,y) = stack.pop...
}
return 1 if (y > grid)
}
}
}
var obj = Percolate()
say 'Sample percolation at 0.6'
obj.percolate(0.6)
obj.site.each { .join.say }
say ''
var tests = 100
say "Doing #{tests} trials at each porosity:"
for p in (0.1..1 `by` 0.1) {
printf("p = %0.1f: %0.3f\n", p, tests.of { obj.percolate(p) }.sum / tests)
}
- Output:
Sample percolation at 0.6
+
+ ▒▒▒ ▒ ▒▒
+ ▒ ▒ ▒ ▒
++++ ▒ ▒ ▒
▒+▒+++++ ▒ ▒
▒ ▒▒▒▒+
▒▒ ▒ ▒ + ▒
▒ ▒+++ ▒ ▒
▒ ▒ ▒+▒+ ▒
▒ ▒ ▒ + ▒ ▒
▒ ▒ +++ ▒▒
▒▒▒ ▒▒▒+▒+▒ ▒ ▒
▒ ▒▒ + ▒ ▒
▒▒ ▒▒+++ ▒ ▒
▒ ▒▒+
▒ ▒ ▒ +
+
Doing 100 trials at each porosity:
p = 0.1: 0.000
p = 0.2: 0.000
p = 0.3: 0.000
p = 0.4: 0.020
p = 0.5: 0.090
p = 0.6: 0.570
p = 0.7: 0.930
p = 0.8: 1.000
p = 0.9: 1.000
p = 1.0: 1.000
Tcl
package require Tcl 8.6
oo::class create SitePercolation {
variable cells w h
constructor {width height probability} {
set w $width
set h $height
for {set cells {}} {[llength $cells] < $h} {lappend cells $row} {
for {set row {}} {[llength $row] < $w} {lappend row $cell} {
set cell [expr {rand() < $probability}]
}
}
}
method print {out} {
array set map {0 "#" 1 " " -1 .}
puts "+[string repeat . $w]+"
foreach row $cells {
set s "|"
foreach cell $row {
append s $map($cell)
}
puts [append s "|"]
}
set outline [lrepeat $w "-"]
foreach index $out {
lset outline $index "."
}
puts "+[join $outline {}]+"
}
method percolate {} {
for {set work {}; set i 0} {$i < $w} {incr i} {
if {[lindex $cells 0 $i]} {lappend work 0 $i}
}
try {
my Fill $work
return {}
} trap PERCOLATED x {
return [list $x]
}
}
method Fill {queue} {
while {[llength $queue]} {
set queue [lassign $queue y x]
if {$y >= $h} {throw PERCOLATED $x}
if {$y < 0 || $x < 0 || $x >= $w} continue
if {[lindex $cells $y $x]<1} continue
lset cells $y $x -1
lappend queue [expr {$y+1}] $x [expr {$y-1}] $x
lappend queue $y [expr {$x-1}] $y [expr {$x+1}]
}
}
}
# Demonstrate one run
puts "Sample percolation, 15x15 p=0.6"
SitePercolation create bp 15 15 0.6
bp print [bp percolate]
bp destroy
puts ""
# Collect statistics
apply {{} {
puts "Percentage of tries that percolate, varying p"
set tries 100
for {set pint 0} {$pint <= 10} {incr pint} {
set p [expr {$pint * 0.1}]
set tot 0
for {set i 0} {$i < $tries} {incr i} {
set bp [SitePercolation new 15 15 $p]
if {[$bp percolate] ne ""} {
incr tot
}
$bp destroy
}
puts [format "p=%.2f: %2.1f%%" $p [expr {$tot*100./$tries}]]
}
}}
- Output:
Sample percolation, 15x15 p=0.6 +...............+ |.##...###.##...| |.#.#####.####..| |............##.| |....###.###.#..| |.#.##..#....#..| |#.........#..#.| |..#...##.##....| |#.#.#....##...#| |###.....#.#...#| |.....##........| |.#.#..## ......| | #..## # .##.#| | # #.# ####...| |# # # # ##...| | ### ## # . | +-------------.-+ Percentage of tries that percolate, varying p p=0.00: 0.0% p=0.10: 0.0% p=0.20: 0.0% p=0.30: 0.0% p=0.40: 0.0% p=0.50: 6.0% p=0.60: 54.0% p=0.70: 98.0% p=0.80: 100.0% p=0.90: 100.0% p=1.00: 100.0%
Wren
import "random" for Random
import "/fmt" for Fmt
var rand = Random.new()
var RAND_MAX = 32767
var EMPTY = ""
var x = 15
var y = 15
var grid = List.filled((x + 1) * (y + 1) + 1, EMPTY)
var cell = 0
var end = 0
var m = 0
var n = 0
var makeGrid = Fn.new { |p|
var thresh = (p * RAND_MAX).truncate
m = x
n = y
grid.clear()
grid = List.filled(m + 1, EMPTY)
end = m + 1
cell = m + 1
for (i in 0...n) {
for (j in 0...m) {
var r = rand.int(RAND_MAX+1)
grid.add((r < thresh) ? "+" : ".")
end = end + 1
}
grid.add("\n")
end = end + 1
}
grid[end-1] = EMPTY
m = m + 1
end = end - m // end is the index of the first cell of bottom row
}
var ff // recursive
ff = Fn.new { |p| // flood fill
if (grid[p] != "+") return false
grid[p] = "#"
return p >= end || ff.call(p + m) || ff.call(p + 1) || ff.call(p - 1) ||
ff.call(p - m)
}
var percolate = Fn.new {
var i = 0
while (i < m && !ff.call(cell + i)) i = i + 1
return i < m
}
makeGrid.call(0.5)
percolate.call()
System.print("%(x) x %(y) grid:")
System.print(grid.join(""))
System.print("\nRunning 10,000 tests for each case:")
for (ip in 0..10) {
var p = ip / 10
var cnt = 0
for (i in 0...10000) {
makeGrid.call(p)
if (percolate.call()) cnt = cnt + 1
}
Fmt.print("p = $.1f: $.4f", p, cnt / 10000)
}- Output:
Sample run:
15 x 15 grid: ..####.#####..# +....####.#.++. .#######.+..+++ +...##...+.++.. ++++..+++.+..++ ....++..+++.+++ +......++.+.+++ .......+++..+.. +.+....+.+..+++ +.+.+...+++..+. .++...+.+...... ..+..++++....++ +.++++.+..+..+. .+..+.+.+...... ..+..+.+.....++ Running 10,000 tests for each case: p = 0.0: 0.0000 p = 0.1: 0.0000 p = 0.2: 0.0000 p = 0.3: 0.0000 p = 0.4: 0.0041 p = 0.5: 0.0918 p = 0.6: 0.5647 p = 0.7: 0.9545 p = 0.8: 0.9997 p = 0.9: 1.0000 p = 1.0: 1.0000
zkl
fcn makeGrid(m,n,p){
grid:=Data((m+1)*(n+1)); // first row and right edges are buffers
grid.write(" "*m); grid.write("\r");
do(n){
do(m){ grid.write(((0.0).random(1)<p) and "+" or "."); } // cell is porous or not
grid.write("\n");
}
grid
}
fcn ff(grid,x,m){ // walk across row looking for a porous cell
if(grid[x]!=43) return(0); // '+' == 43 ASCII == porous
grid[x]="#";
return(x+m>=grid.len() or
ff(grid,x+m,m) or ff(grid,x+1,m) or ff(grid,x-1,m) or ff(grid,x-m,m));
}
fcn percolate(grid,m){
x:=m+1; i:=0; while(i<m and not ff(grid,x,m)){ x+=1; i+=1; }
return(i<m); // percolated through the grid?
}
grid:=makeGrid(15,15,0.60);
println("Did liquid percolate: ",percolate(grid,15));
println("15x15 grid:\n",grid.text);
println("Running 10,000 tests for each case:");
foreach p in ([0.0 .. 1.0, 0.1]){
cnt:=0.0; do(10000){ cnt+=percolate(makeGrid(15,15,p),15); }
"p=%.1f: %.4f".fmt(p, cnt/10000).println();
}- Output:
Did liquid percolate: True 15x15 grid: .###.##.#++..++ ......+###..+.+ +...+...##..+++ ++..+.+.#+.+.++ ..+++###..+..++ .+.##..++.+..++ .+#.+..++++++.. +####+..+....++ .#.#..+..++.+.+ #.#++++.+++.+++ +#++..+.+.+.+++ #######..++++++ #.##.#+++...+.. +.#.#+++.++.+++ +.+#+.++..+..++ Running 10,000 tests for each case: p=0.0: 0.0000 p=0.1: 0.0000 p=0.2: 0.0000 p=0.3: 0.0000 p=0.4: 0.0006 p=0.5: 0.0304 p=0.6: 0.2989 p=0.7: 0.8189 p=0.8: 0.9903 p=0.9: 1.0000 p=1.0: 1.0000