Babylonian spiral: Difference between revisions
Nim solution.
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(Nim solution.) |
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Plots.plot(babylonian_spiral(10_000))
</syntaxhighlight>
=={{header|Nim}}==
{{trans|Python}}
{{libheader|gnuplotlib.nim}}
<syntaxhighlight lang="Nim">import std/[math, strformat, strutils]
type Vector = tuple[x, y: int]
func `+`(a, b: Vector): Vector =
## Return the sum of two vectors.
(a.x + b.x, a.y + b.y)
func isqrt(n: int): int =
## Return the integer square root of "n".
int(sqrt(n.toFloat))
proc babylonianSpiral(nsteps: int): seq[Vector] =
## Get the points for each step along a Babylonia spiral of `nsteps` steps.
## Origin is at (0, 0) with first step one unit in the positive direction along
## the vertical (y) axis. The other points are selected to have integer x and y
## coordinates, progressively concatenating the next longest vector with integer
## x and y coordinates on the grid. The direction change of the new vector is
## chosen to be nonzero and clockwise in a direction that minimizes the change
## in direction from the previous vector.
var xyDeltas: seq[Vector] = @[(0, 0), (0, 1)]
var δsquared = 1
for _ in 0..nsteps - 3:
let (x, y) = xyDeltas[^1]
let θ = arctan2(y.toFloat, x.toFloat)
var candidates: seq[Vector]
while candidates.len == 0:
inc δsquared, 1
for i in 0..<nsteps:
let a = i * i
if a > δsquared div 2:
break
for j in countdown(isqrt(δsquared) + 1, 1):
let b = j * j
if a + b < δsquared:
break
if a + b == δsquared:
candidates.add [(i, j), (-i, j), (i, -j), (-i, -j), (j, i), (-j, i), (j, -i), (-j, -i)]
var p: Vector
var minVal = TAU
for candidate in candidates:
let val = floorMod(θ - arctan2(candidate.y.toFloat, candidate.x.toFloat), TAU)
if val < minVal:
minVal = val
p = candidate
xyDeltas.add p
result = cumsummed(xyDeltas)
let points10000 = babylonianSpiral(10_000)
### Task ###
echo "The first 40 Babylonian spiral points are:"
for i, p in points10000[0..39]:
stdout.write alignLeft(&"({p.x}, {p.y})", 10)
stdout.write if (i + 1) mod 10 == 0: "\n" else: ""
### Stretch task ###
import gnuplot
var x, y: seq[float]
for p in points10000:
x.add p.x.toFloat
y.add p.y.toFloat
withGnuPlot:
plot(x, y, "Babylonian spiral", "with lines lc black lw 1")
png("babylonian_spiral.png")
</syntaxhighlight>
{{out}}
<pre>The first 40 Babylonian spiral points are:
(0, 0) (0, 1) (1, 2) (1, 2) (3, 2) (5, 1) (5, 1) (5, 1) (7, -1) (7, -4)
(6, -7) (6, -7) (6, -7) (4, -10) (4, -10) (4, -10) (0, -10) (-4, -9) (-7, -6) (-7, -6)
(-9, -2) (-9, -2) (-9, -2) (-9, -2) (-9, -2) (-9, 3) (-8, 8) (-8, 8) (-8, 8) (-6, 13)
(-6, 13) (-6, 13) (-2, 17) (-2, 17) (3, 20) (3, 20) (9, 20) (15, 19) (15, 19) (15, 19)
</pre>
=={{header|Perl}}==
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