DrawBot: Create an animated flower-like pattern by drawing circles on a donut.

PsychoDonut.py

# nCirclesH = 18; nCirclesV = 6:
#   http://dailydrawbot.tumblr.com/post/138985675364/psychodonut-2
# nCirclesH = 38; nCirclesV = 28:
#   http://dailydrawbot.tumblr.com/post/139047595845/psychodonut-3

def project(x, y, innerR, outerR, phase):
    # convert from "donut space" to normal space
    angle = 2 * pi * x
    f = (cos(phase + pi * y) + 1) / 2
    R = innerR + f * (outerR - innerR)
    x1 = R * cos(angle)
    y1 = R * sin(angle)
    return x1, y1

def projectZ(y, phase):
    return sin(phase + pi * y)

nCirclesH = 18  # must be even
nCirclesV = 6   # ditto

canvasSize = 500
nFrames = 50

for frame in range(nFrames):
    framePhase = frame / nFrames
    newPage(canvasSize, canvasSize)
    frameDuration(1/20)
    rect(0, 0, canvasSize, canvasSize)
    translate(canvasSize/2, canvasSize/2)

    phase = -2 * pi * framePhase / nCirclesV
    outerR = 0.48 * canvasSize
    innerR = 0.0 * canvasSize

    nGap = 6
    steps = 35
    circleW = 0.5 / nCirclesH
    circleH = 1 / nCirclesV
    polygons = []
    for j in range(nCirclesV):
        for i in range(nCirclesH):
            if (i + j) % 2:
                cx = i / nCirclesH - framePhase / nCirclesH
                cy = 2 * j / nCirclesV
                poly = []
                for k in range(steps):
                    angle = 2 * pi * k / steps
                    x = cx + circleW * cos(angle)
                    y = cy + circleH * sin(angle)
                    poly.append((x, y))

                poly = [project(x, y, innerR, outerR, phase) for x, y in poly]
                polygons.append((projectZ(cy, phase), poly))

    polygons.sort()

    for y, pol in polygons:
        gray = 0.1 + y/2.5 + 0.5
        fill(gray, 0.3 + 0.7*gray, 0.9)
        polygon(*pol)

saveImage("PsychoDonut.gif")