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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")
```