Red curve: Helix ; Blue curve: super-helix (helix around another helix) ; Green curve: hyper-helix?
Python, 50 lines
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Copy to clipboard1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | # SuperHelix
# FB - 201007213
import math
from PIL import Image
imgx = 800
imgy = 800
image = Image.new("RGB", (imgx, imgy))
r0 = float(300) # radius of the 1. helix
r1 = float(30) # radius of the 2. helix
r2 = float(10) # radius of the 3. helix
ctr = 0
while True:
ctr += 1
# 1. helix point
a0 = float(ctr) / r0 / 10
x0 = r0 * math.cos(a0)
y0 = r0 * math.sin(a0)
z0 = float(ctr) * 0.01
# plot the 1. helix point
if z0 > imgy - 1: break
image.putpixel((x0 + imgx / 2, z0), (255, 0, 0))
# 2. helix point (superhelix)
a1 = float(ctr) / r1 / 2
x1 = x0 + r1 * math.cos(a1) * math.cos(a0)
y1 = y0 + r1 * math.cos(a1) * math.sin(a0)
z1 = z0 + r1 * math.sin(a1)
# plot the 2. helix point
if z1 < 0: z1 = 0
if z1 > imgy - 1: break
image.putpixel((x1 + imgx / 2, z1), (0, 0, 255))
# 3. helix point (hyperhelix?)
a2 = float(ctr) / r2
x2 = x1 + r2 * math.cos(a2) * math.cos(a1)
y2 = y1 + r2 * math.cos(a2) * math.sin(a1)
z2 = z1 + r2 * math.sin(a2)
# plot the 3. helix point
if z2 < 0: z2 = 0
if z2 > imgy - 1: break
image.putpixel((x2 + imgx / 2, z2), (0, 255, 0))
image.save("SuperHelix.png", "PNG")
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I had to convert each component of the coordinate passed in the first tuple argument to all the image.putpixel() method calls into integer to avoid a TypeError exception. For example the first one:
changed to:
Even with this extra overhead, it still creates the image quickly.