Added Pi-approximating automatons.
authorEugen Sawin <sawine@me73.com>
Thu, 30 Dec 2010 02:16:10 +0100
changeset 2ccbf96145796
parent 1 2e65c867022c
child 3 89d76549ba6e
Added Pi-approximating automatons.
anks.py
cellpimat.py
marshal.py
render.py
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/anks.py	Thu Dec 30 02:16:10 2010 +0100
     1.3 @@ -0,0 +1,72 @@
     1.4 +class Cell(object):
     1.5 +	def __init__(self, value):
     1.6 +		self.value = value
     1.7 +	def __str__(self):
     1.8 +		if self.value:
     1.9 +			return chr(176)
    1.10 +		else:
    1.11 +			return chr(177)
    1.12 +
    1.13 +def iterate(grid, rule):
    1.14 +	expanded = [Cell(False), Cell(False)]
    1.15 +	expanded.extend(grid)
    1.16 +	expanded.extend([Cell(False), Cell(False)])
    1.17 +	new_grid = []
    1.18 +	for i in xrange(len(expanded)-2):
    1.19 +		triple = expanded[i:i+3]
    1.20 +		#print [t.value for t in triple]
    1.21 +		
    1.22 +		if triple[0].value and triple[1].value and triple[2].value:
    1.23 +			new_grid.append(Cell(rule[7]))
    1.24 +		elif triple[0].value and triple[1].value:
    1.25 +			new_grid.append(Cell(rule[6]))
    1.26 +		elif triple[0].value and triple[2].value:
    1.27 +			new_grid.append(Cell(rule[5]))
    1.28 +		elif triple[0].value:
    1.29 +			new_grid.append(Cell(rule[4]))
    1.30 +		elif triple[1].value and triple[2].value:
    1.31 +			new_grid.append(Cell(rule[3]))
    1.32 +		elif triple[1].value:
    1.33 +			new_grid.append(Cell(rule[2]))
    1.34 +		elif triple[2].value:
    1.35 +			new_grid.append(Cell(rule[1]))
    1.36 +		else:
    1.37 +			new_grid.append(Cell(rule[0]))
    1.38 +	return new_grid
    1.39 +
    1.40 +def show(grid, max_cells):
    1.41 +	import sys
    1.42 +	padding_left = int(0.5 + max_cells - len(grid)) / 2
    1.43 +	padding_right = (max_cells - len(grid)) / 2
    1.44 +	for i in xrange(padding_left):
    1.45 +		sys.stdout.write(chr(178))
    1.46 +	for cell in grid:
    1.47 +		sys.stdout.write(str(cell))
    1.48 +	for i in xrange(padding_right):
    1.49 +		sys.stdout.write(chr(178))
    1.50 +	print
    1.51 +
    1.52 +def gen_rule(i):
    1.53 +	rule = []
    1.54 +	v = i
    1.55 +	for x in range(8):
    1.56 +		rule.append(v - v/2*2)
    1.57 +		v = v/2
    1.58 +	return rule
    1.59 +
    1.60 +def main():
    1.61 +	import time
    1.62 +
    1.63 +	max_iter = 150
    1.64 +	max_cells = max_iter * 2 + 1
    1.65 +	for i in xrange(255):
    1.66 +		rule = gen_rule(i)
    1.67 +		print "rule %i" % i
    1.68 +		grid = [Cell(True)]
    1.69 +		for i in range(max_iter):
    1.70 +			show(grid, max_cells)
    1.71 +			grid = iterate(grid, rule)
    1.72 +		#time.sleep(2)
    1.73 +
    1.74 +if __name__ == "__main__":
    1.75 +	main()
     2.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     2.2 +++ b/cellpimat.py	Thu Dec 30 02:16:10 2010 +0100
     2.3 @@ -0,0 +1,175 @@
     2.4 +class Grid(object):
     2.5 +
     2.6 +	def __init__(self):
     2.7 +		self.cells = {}
     2.8 +		self.minx = 0
     2.9 +		self.maxx = 0
    2.10 +		self.miny = 0
    2.11 +		self.maxy = 0
    2.12 +
    2.13 +	def set(self, pos, value=1):
    2.14 +		if not pos in self.cells or value != self.cells[pos]:
    2.15 +			self.cells[pos] = value
    2.16 +			self.update(pos)
    2.17 +		return self
    2.18 +
    2.19 +	def clear(self, pos):
    2.20 +		if pos in self.cells:
    2.21 +			del self.cells[pos]
    2.22 +			self.update(pos)
    2.23 +		return self
    2.24 +
    2.25 +	def update(self, (x, y)):
    2.26 +		self.minx = min(x, self.minx)
    2.27 +		self.maxx = max(x, self.maxx)
    2.28 +		self.miny = min(y, self.miny)
    2.29 +		self.maxy = max(y, self.maxy)
    2.30 +		return self
    2.31 +
    2.32 +	def width(self):
    2.33 +		return self.maxx - self.minx + 1
    2.34 +
    2.35 +	def height(self):
    2.36 +		return self.maxy - self.miny + 1
    2.37 +
    2.38 +	def __len__(self):
    2.39 +		return len(self.cells)
    2.40 +
    2.41 +	def __str__(self):
    2.42 +		pass
    2.43 +
    2.44 +import copy
    2.45 +
    2.46 +class Rule(object):
    2.47 +
    2.48 +	def iterate(self, oldgrid):
    2.49 +		grid = copy.deepcopy(oldgrid)
    2.50 +		for x in xrange(oldgrid.minx - 1, oldgrid.maxx + 2):
    2.51 +			for y in xrange(oldgrid.miny - 1, oldgrid.maxy + 2):
    2.52 +				#print x, y, self.neighbours(oldgrid, x, y)
    2.53 +				n = self.neighbours(oldgrid, (x, y))
    2.54 +				if n > 2:
    2.55 +					grid.set((x, y))					
    2.56 +		return grid
    2.57 +
    2.58 +	def neighbours(self, grid, (testx, testy)):
    2.59 +		n = 0
    2.60 +		#print "testing ", testx, testy
    2.61 +		for x in range(testx - 1, testx + 2):
    2.62 +			for y in range(testy - 1, testy + 2):
    2.63 +				if (x, y) in grid.cells:
    2.64 +					n += 1
    2.65 +				#print x, y, n
    2.66 +		return n 
    2.67 +	
    2.68 +
    2.69 +class Rule2(object):
    2.70 +
    2.71 +	def iterate(self, oldgrid):
    2.72 +		grid = copy.deepcopy(oldgrid)
    2.73 +		for x in xrange(oldgrid.minx - 1, oldgrid.maxx + 2):
    2.74 +			for y in xrange(oldgrid.miny, oldgrid.maxy + 2):
    2.75 +				#print "testing ", x, y,
    2.76 +				if (x+1, y) in oldgrid.cells or (x, y-1) in oldgrid.cells:
    2.77 +					grid.set((x, y), 1)								
    2.78 +		return grid
    2.79 +
    2.80 +import random
    2.81 +import marshal
    2.82 +
    2.83 +class PotentialGrowth(object):
    2.84 +		
    2.85 +	def __init__(self):
    2.86 +		random.seed()
    2.87 +
    2.88 +	def iterate(self, oldgrid):
    2.89 +		grid = copy.deepcopy(oldgrid)
    2.90 +		for cell in oldgrid.cells.iteritems():
    2.91 +			pos = cell[0]
    2.92 +			value = cell[1]
    2.93 +			if value > 1:
    2.94 +				new_pos, new_value = self.grow(grid, pos)
    2.95 +				grid.set(new_pos, new_value)
    2.96 +				grid.set(pos, value - 1)
    2.97 +		return grid
    2.98 +
    2.99 +	def grow(self, grid, (x, y)):
   2.100 +		neighbours = [(x-1, y), (x, y+1), (x+1, y), (x, y-1)]
   2.101 +		neighbours = [n for n in neighbours if n not in grid.cells]
   2.102 +		try:
   2.103 +			pos = random.choice(neighbours)	
   2.104 +			value = 4
   2.105 +		except IndexError:
   2.106 +			pos = (x, y)
   2.107 +			value = grid.cells[pos]
   2.108 +		return pos, value
   2.109 +
   2.110 +import sys
   2.111 +import math
   2.112 +
   2.113 +def ruleTest():
   2.114 +	rule = Rule()
   2.115 +	grid = Grid()
   2.116 +	grid.set((0, 0))
   2.117 +	grid.set((0, 1)).set((1, 0)).set((0, -1)).set((-1, 0))
   2.118 +	
   2.119 +	
   2.120 +	print "iteration radius(diff) area(diff) pi"
   2.121 +
   2.122 +	iterations = int(sys.argv[1])
   2.123 +
   2.124 +	for i in range(iterations):
   2.125 +		A = len(grid)
   2.126 +		r = grid.width() / 2.0
   2.127 +		r_ideal = math.sqrt(A / math.pi)
   2.128 +		A_ideal = r**2 * math.pi
   2.129 +		pi = A / r**2
   2.130 +		print "%i %f(%f) %i(%i) %f" % (i, r, r - r_ideal, 
   2.131 +										A, A - A_ideal, pi)
   2.132 +
   2.133 +		grid = rule.iterate(grid)
   2.134 +		dumpGrid(grid, "grid.cfg")
   2.135 +		#print
   2.136 +
   2.137 +def rule2Test():
   2.138 +	rule = Rule2()
   2.139 +	grid = Grid()
   2.140 +	grid.set((0, 0)).set((-1, 0)).set((0, 1))
   2.141 +	olda = 1
   2.142 +
   2.143 +	iterations = int(sys.argv[1])
   2.144 +
   2.145 +	for i in range(iterations):
   2.146 +		a =  (float(len(grid)) - grid.width()) * 4.0
   2.147 +		pi = 1.0 / ((grid.width()-1)**2 / ((a + olda) / 2.0))
   2.148 +		print i, grid.width(), len(grid), pi
   2.149 +		grid = rule.iterate(grid)
   2.150 +		olda = a
   2.151 +		dumpGrid(grid, "grid.cfg")
   2.152 +
   2.153 +def potentialTest():
   2.154 +	rule = PotentialGrowth()
   2.155 +	grid = Grid()
   2.156 +	grid.set((0, 0), 4)
   2.157 +
   2.158 +	iterations = int(sys.argv[1])
   2.159 +
   2.160 +	for i in range(iterations):
   2.161 +		A = len(grid)
   2.162 +		r = grid.width() / 4.0 + grid.height() / 4.0
   2.163 +		r_ideal = math.sqrt(A / math.pi)
   2.164 +		A_ideal = r**2 * math.pi
   2.165 +		pi = A / r**2
   2.166 +		print "%i %f(%f) %i(%i) %f" % (i, r, r - r_ideal, 
   2.167 +										A, A - A_ideal, pi)
   2.168 +
   2.169 +		grid = rule.iterate(grid)
   2.170 +		dumpGrid(grid, "grid.cfg")
   2.171 +
   2.172 +def main():
   2.173 +	ruleTest()
   2.174 +	#rule2Test()
   2.175 +	#potentialTest()
   2.176 +
   2.177 +if __name__ == "__main__":
   2.178 +	main()
     3.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     3.2 +++ b/marshal.py	Thu Dec 30 02:16:10 2010 +0100
     3.3 @@ -0,0 +1,36 @@
     3.4 +import ConfigParser
     3.5 +
     3.6 +meta_section = "meta"
     3.7 +data_section = "cells"
     3.8 +
     3.9 +def dumpGrid(grid, filename):
    3.10 +	config = ConfigParser.RawConfigParser()
    3.11 +
    3.12 +	config.add_section(meta_section)
    3.13 +	config.set(meta_section, 'min x', grid.minx)
    3.14 +	config.set(meta_section, 'max x', grid.maxx)
    3.15 +	config.set(meta_section, 'min y', grid.miny)
    3.16 +	config.set(meta_section, 'max y', grid.maxy)
    3.17 +	config.set(meta_section, 'cell no', len(grid))	
    3.18 +	
    3.19 +	config.add_section(data_section)
    3.20 +	config.set(data_section, "cells", ";".join([str(pos) for pos in grid.cells.iterkeys()]))
    3.21 +
    3.22 +	with open(filename, 'wb') as configfile:
    3.23 +		config.write(configfile)
    3.24 +
    3.25 +def loadGrid(filename):
    3.26 +	config = ConfigParser.RawConfigParser()
    3.27 +	config.read(filename)
    3.28 +
    3.29 +	grid = Grid()
    3.30 +	grid.minx = config.getint(meta_section, "min x")
    3.31 +	grid.maxx = config.getint(meta_section, "max x")
    3.32 +	grid.miny = config.getint(meta_section, "min y")
    3.33 +	grid.maxy = config.getint(meta_section, "max y")
    3.34 +
    3.35 +	cells = config.get(data_section, "cells")
    3.36 +	for cell in cells.split(";"):
    3.37 +		cell = [int(cell.strip("(),")) for cell in cell.split()]
    3.38 +		grid.cells[(cell[0], cell[1])] = 1
    3.39 +	return grid
     4.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     4.2 +++ b/render.py	Thu Dec 30 02:16:10 2010 +0100
     4.3 @@ -0,0 +1,39 @@
     4.4 +import Tkinter as tk
     4.5 +
     4.6 +class Render(object):
     4.7 +	def __init__(self, title, width, height):
     4.8 +		self.title = title		
     4.9 +		self.width = width
    4.10 +		self.height = height
    4.11 +		self.root = tk.Tk(className=title, sync=1)
    4.12 +		self.canvas = tk.Canvas(width=self.width, height=self.height, bg="black")
    4.13 +		self.canvas.pack(expand=tk.YES, fill=tk.BOTH)
    4.14 +	def render(self, grid):
    4.15 +		offset = (self.width / 2, self.height / 2)
    4.16 +		size = 1
    4.17 +		cell_ids = []
    4.18 +		for pos in grid.cells.iterkeys():
    4.19 +			x = pos[0] + offset[0]
    4.20 +			y = pos[1] + offset[1]
    4.21 +			cell_id = self.canvas.create_rectangle(x, y, x+size, y+size, 
    4.22 +					fill="yellow", width=0)
    4.23 +			cell_ids.append(cell_id)
    4.24 +		self.root.update()
    4.25 +		for cell_id in cell_ids:
    4.26 +			self.canvas.delete(cell_id)
    4.27 +
    4.28 +import sys
    4.29 +import time
    4.30 +import cellpimat
    4.31 +
    4.32 +def main():
    4.33 +	filename = sys.argv[1]
    4.34 +	print "rendering ", filename	
    4.35 +	render = Render("hope", 800, 800)
    4.36 +	while True:
    4.37 +		grid = cellpimat.loadGrid(filename)
    4.38 +		render.render(grid)
    4.39 +		time.sleep(1)
    4.40 +
    4.41 +if __name__ == "__main__":
    4.42 +	main()