Sierpinski Triangle

Having recently heard something about chaos theory, I was interested in the sierpinski triangle. Specifically in the random generation. To proof, if it can really be generated using a dice, I wrote this program.

How it works

• You start with any point inside the triangle (I chose the center)
• A triangle has three points, let us call them A, B and C
• You choose randomly between one of those three points, go half the distance and set a pixel right there
• Repeating this process over and over again (always starting at your last point), you eventually get the sierpinski triangle

Controls

• Space toggles if the triangle is generated
• m toggles if the current position is shown (indicated by a blue circle)

``````# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 15th of July, 2015``````

``````# importing needed modules
import pygame, sys, time, math, os, random

""" CLASSES """
# dummy class for global variables
class dummy():
pass

""" FUNCTIONS """
# gets the position on a circle
# circle center                           : '_pos'
# angle from center to point on the circle: '_angle'
return [
]

# returns an integer version of given positon
def intpos(_pos):
return [int(_pos[0]), int(_pos[1])]

# basic vector functions
def vecConvert(p1, p2):
return [p2[0] - p1[0], p2[1] - p1[1]]
def vecLen(vec):
return math.sqrt( (vec[0]**2) + (vec[1]**2) )
def vecMultiply(vec, n):
return [vec[0] * n, vec[1] * n]
def vecGetPoint(vec, point):
return [point[0] + vec[0], point[1] + vec[1]]
return [vec1[0] + vec2[0], vec1[1] + vec2[1]]

# quits the program
def quit():
sys.exit()

""" TICK; RENDER """
# tick function
def tick():
# handle events
for event in pygame.event.get():
# quit
if event.type == pygame.QUIT:
quit()

# keydown
if event.type == pygame.KEYDOWN:
# toggle running
if event.key == pygame.K_SPACE:
if main.RUNNING:
main.RUNNING = False
else:
main.RUNNING = True

# toggle showing the current pos
if event.key == pygame.K_m:
if main.SHOWPOS:
main.SHOWPOS = False
else:
main.SHOWPOS = True

# render function
def render():
# calculate and render
if main.RUNNING:
# for loop speeds up the drawing of the triangle
for _ in range(0, 10):
# consider which point to go to
r = random.randint(0, 2)
if r == 0:
vec = vecConvert(main.POS, main.A)
elif r == 1:
vec = vecConvert(main.POS, main.B)
elif r == 2:
vec = vecConvert(main.POS, main.C)

# calculate the next point using vectors
vecl = vecLen(vec)
if vecl != 0:
vec0 = vecMultiply(vec, 1./vecl)
vecn = vecMultiply(vec0, vecl/2.)
main.LASTPOS = main.POS[:]
main.POS = vecGetPoint(vecn, main.POS)

# draw actual pixel
main.SURF.set_at(intpos(main.POS), main.DOTCOLOR)

# blit surface
main.SCREEN.blit(main.SURF, [0, 0])

# render current position
if main.SHOWPOS:
pygame.draw.circle(main.SCREEN, main.POSCOLOR, intpos(main.POS), 10)

# flip
pygame.display.flip()

""" INIT """
# initialize program
def init():
main.WIDTH, main.HEIGHT = 720, 720
main.SIZE = [main.WIDTH, main.HEIGHT]
main.CENTER = [main.WIDTH / 2., main.HEIGHT / 2.]
main.SCREEN = pygame.display.set_mode(main.SIZE)
main.SURF = pygame.Surface(main.SIZE)

main.CAPTION = "Sierpinski Triangle"
main.TICKS = 0

main.BACKCOLOR = (0, 0, 0)
main.DOTCOLOR = (255, 255, 255)
main.POSCOLOR = (50, 50, 200)

n = 300
angle = 0
main.A = getCirclePos(main.CENTER, n, 360. / 3 * 0 + angle)
main.B = getCirclePos(main.CENTER, n, 360. / 3 * 1 + angle)
main.C = getCirclePos(main.CENTER, n, 360. / 3 * 2 + angle)

main.LASTPOS = main.CENTER[:]
main.POS = main.CENTER[:]

main.RUNNING = False
main.SHOWPOS = True

# functions
pygame.display.set_caption(main.CAPTION)
main.SURF.fill(main.BACKCOLOR)

pygame.draw.line(main.SURF, main.DOTCOLOR, main.A, main.B)
pygame.draw.line(main.SURF, main.DOTCOLOR, main.B, main.C)
pygame.draw.line(main.SURF, main.DOTCOLOR, main.C, main.A)

""" RUN """
# run function (uses tick() and render())
def run():
ticksPerSecond = 60
lastTime = time.time() * 1000000000
nsPerTick =  1000000000.0 / float(ticksPerSecond)

ticks = 0
frames = 0

lastTimer = time.time() * 1000
delta = 0.0

while True:
now = time.time() * 1000000000
delta += float(now - lastTime) / float(nsPerTick)
lastTime = now
shouldRender = False

while delta >= 1:
ticks += 1
main.TICKS += 1
tick()
delta -= 1
shouldRender = True

if shouldRender:
frames += 1
render()

if time.time() * 1000 - lastTimer >= 1000:
lastTimer += 1000

# debug
# print("Frames: " + str(frames) + ", ticks: " + str(ticks))

frames = 0
ticks = 0

# main variable
main = dummy()
init()

# start program
run()``````