Menger Sponge

Normally the Menger Sponge is a three-dimensional cuboid. This program works in a two-dimensional space, so it only shows one side of the sponge.
Because a computer has its capacities, I capped the maximum square count to 10,000. After that maximum, the face will not be complete.

Controls

  • Space divides every square once again

Iteration 0 Iteration 1 Iteration 2 Iteration 3 Iteration 4


# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 20th of July, 2015
#         edited 22nd 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 mouse position
def getMousePos():
	p = pygame.mouse.get_pos()
	return [p[0], p[1]]

# validates color integer
# extra feature: _min and _max implementation
def colorValid(_color, _min = 0, _max = 255):
	newColor = math.fabs(_color)
	n = _max - _min
	if newColor > n:
		if int(newColor / n) % 2 == 0:
			newColor = newColor % n
		else:
			newColor = n - (newColor % n)
	
	return int(newColor) + _min

# gets the position on a circle
# circle center                           : '_pos'
# circle radius                           : '_radius'
# angle from center to point on the circle: '_angle'
def getCirclePos(_pos, _radius, _angle):
	return [
				_pos[0] + _radius * math.cos(math.radians(_angle)),
				_pos[1] + _radius * math.sin(math.radians(_angle))
			]

# 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]]
def vecAdd(vec1, vec2):
	return [vec1[0] + vec2[0], vec1[1] + vec2[1]]

# calculates distance between given positions
def posDistance(p1, p2):
	return math.sqrt( (p2[0] - p1[0])**2 + (p2[1] - p1[1])**2 )

# 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()
		
		# keyup
		if event.type == pygame.KEYUP:
			# handle 'main.KEYSDOWN'
			if event.key in main.KEYSDOWN:
				main.KEYSDOWN.remove(event.key)
		
		# keydown
		if event.type == pygame.KEYDOWN:
			# handle 'main.KEYSDOWN'
			if event.key not in main.KEYSDOWN:
				main.KEYSDOWN.append(event.key)
			
			if event.key == pygame.K_SPACE:
				squares = []
				for _ in main.SQUARES:
					w, h = _[2] / 3, _[3] / 3
					squares.append( [_[0], _[1], w, h] )
					squares.append( [_[0]+w, _[1], w, h] )
					squares.append( [_[0]+w+w, _[1], w, h] )
					squares.append( [_[0], _[1]+h, w, h] )
					squares.append( [_[0]+w+w, _[1]+h, w, h] )
					squares.append( [_[0], _[1]+h+h, w, h] )
					squares.append( [_[0]+w, _[1]+h+h, w, h] )
					squares.append( [_[0]+w+w, _[1]+h+h, w, h] )
					
					if len(squares) > 10000:
						break
				main.SQUARES = squares

# render function
def render():
	# fill
	main.SURF.fill(main.COLOR)
	
	for _ in main.SQUARES:
		#pygame.draw.rect(main.SURF, (50+(random.randint(-1, 1)*20), 50, 200), _)
		pygame.draw.rect(main.SURF, (50, 50, 200), _)
	
	# blit and flip
	main.SCREEN.blit(main.SURF, [0, 0])
	pygame.display.flip()

""" INIT """
# initialize program
def init():
	main.WIDTH, main.HEIGHT = 600, 600
	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 = "Menger Sponge"
	main.COLOR = (0, 0, 0)
	main.TICKS = 0
	main.KEYSDOWN = []
	
	main.SQUARES = [
		[0, 0, main.WIDTH, main.HEIGHT]
	]
	
	# functions
	pygame.display.set_caption(main.CAPTION)

""" 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()
Advertisements

One thought on “Menger Sponge

  1. Pingback: Menger Sponge II – J-Blog

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s