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Dynamical Billiards Simulation (Python recipe) by Steve Wadley
Forked from Recipe 577445 (I am learning Python 3.3 for fun and am interested in how Python handles graphics and physics. Thank you)
ActiveState Code (http://code.activestate.com/recipes/578572/)

It simulates reflections of a ball on a billiards table that has one or more circular obstacles. (This can also be thought as a 2d ray-tracing.)

Most of the time the path of the ball would be chaotic (meaning, if another ball started from any slightly different location or direction then its path would be very different after a short while).

See Wikipedia for more info: http://en.wikipedia.org/wiki/Dynamical_billiards

Python, 89 lines
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# Dynamical Billiards Simulation
# FB - 201010295
# See Wikipedia for more info:
# http://en.wikipedia.org/wiki/Dynamical_billiards
import math
import random
from PIL import Image, ImageDraw
imgx = 800
imgy = 600
image = Image.new("RGB", (imgx, imgy))
draw = ImageDraw.Draw(image)

# Only 1 ball is used!
maxSteps = 20000 # of steps of ball motion (in constant speed)

n = random.randint(1, 7) # of circular obstacles
crMax = int(min(imgx - 1, imgy - 1) / 4) # max circle radius
crMin = 10 # min circle radius

# create circular obstacle(s)
cxList = []
cyList = []
crList = []
for i in range(n):
    while(True): # circle(s) must not overlap
        cr = random.randint(crMin, crMax) # circle radius
        cx = random.randint(cr, imgx - 1 - cr) # circle center x
        cy = random.randint(cr, imgy - 1 - cr) # circle center y
        flag = True
        if i > 0:
            for j in range(i):
                if math.hypot(cx - cxList[j], cy - cyList[j]) < cr + crList[j]:
                    flag = False
                    break
        if flag == True:
            break
    draw.ellipse((cx - cr, cy - cr, cx + cr, cy + cr))
    cxList.append(cx)
    cyList.append(cy)
    crList.append(cr)

# initial location of the ball must be outside of the circle(s)
while(True):
    x = float(random.randint(0, imgx - 1))
    y = float(random.randint(0, imgy - 1))
    flag = False
    for i in range(n):
        if math.hypot(x - cxList[i], y - cyList[i]) <= crList[i]:
            flag = True
            break
    if flag == False:
        break
    
# initial direction of the ball
a = 2.0 * math.pi * random.random()
s = math.sin(a)
c = math.cos(a)

for i in range(maxSteps):
    image.putpixel((int(x), int(y)), (255, 255, 255))
    xnew = x + c
    ynew = y + s

    # reflection from the walls
    if xnew < 0 or xnew > imgx - 1:
        c = -c
        xnew = x
    if ynew < 0 or ynew > imgy - 1:
        s = -s
        ynew = y

    # reflection from the circle(s)
    for i in range(n):
        if math.hypot(xnew - cxList[i], ynew - cyList[i]) <= crList[i]:
            # angle of the circle point
            ca = math.atan2(ynew - cyList[i], xnew - cxList[i])
            # reversed collision angle of the ball
            rca = math.atan2(-s, -c)
            # reflection angle of the ball
            rab = rca + (ca - rca) * 2
            s = math.sin(rab)
            c = math.cos(rab)
            xnew = x
            ynew = y

    x = xnew
    y = ynew
    
image.save("Dynamical_Billiards.png", "PNG")
Tags: chaos, graphics, math, pil, random