Python script for generating doming tiling of Aztec diamond

readme.md

This algorithm is ported from Eric Nordenstam's C++ script into Python. The program writes an scalable-vector-graphics (SVG) file, but would like to write as d3.js.

If you wish to learn more about dominos and determinantal processes you're encouraged to check his work and his advisors:

• math/9801068:Random Domino Tilings and the Arctic Circle Theorem
• math/9906120:Discrete orthogonal polynomial ensembles and the Plancherel measure
• arXiv:0802.2592 On the Shuffling Algorithm for Domino Tilings

Lately there has been exciting work in determinantal processes. Just to name one:

• arXiv:1111.4408 Macdonald processes

It would be nice to write more computational software, perhaps in numPy or Pandas instead of Mathematica.

domino.py

import random
class aztecDiamond:
  def __init__(self,x):
		if(type(x)==type(0)):
			n = x
			board = dict()
			for k in range(1,2*n+1):
				l = min(2*k,4*n-2*k+2)
				for j in range(l):
					board[(j+  0.5 - l/2,k-n - 0.5)] = "x"
			board[0]=n
			self.tile = board
		elif(type(x)==type('')):
			b = x
			sq = b.split("\n")
			board = dict()
			n = len(sq)/2
			for k in range(1,2*n+1):
				l = min(2*k,4*n-2*k+2)
				row = sq[k-1].replace(".","")
				for j in range(l):
					board[(j+  0.5 - l/2,k-n - 0.5)] = row[j]
			board[0]= len(sq)/2
			self.tile = board
	
	def removeBadBlocks(self):
		bd = self.tile
		n = bd[0]
		for k in range(1,2*n+1):
			l = min(2*k,4*n-2*k+2)
			for j in range(l):
				a,b = j+  0.5 - l/2,k-n - 0.5
				try:
					if( (bd[(a,b)].lower()=='s' and	bd[(a+1,b)].lower()=='s' and bd[(a,b+1)].lower()=='n' and bd[(a+1,b+1)].lower()=='n') or
					(bd[(a,b)].lower()=='e' and bd[(a+1,b)].lower()=='w' and bd[(a,b+1)].lower()=='e' and bd[(a+1,b+1)].lower()=='w')):
						bd[(a,b)]='x'
						bd[(a+1,b)]='x'
						bd[(a,b+1)]='x'
						bd[(a+1,b+1)]='x'
				except:
					pass
		self.tile = bd
		return self
		
	def fillGoodBlocks(self):
		bd = self.tile
		n = bd[0]
		for k in range(1,2*n+1-1):
			l = min(2*k,4*n-2*k+2)
			for j in range(l-1):
				a,b = j+  0.5 - l/2,k-n - 0.5
				if( bd[(a,b)]=='x' and bd[(a+1,b)]=='x' and bd[(a,b+1)]=='x' and bd[(a+1,b+1)]=='x'):
					if(random.random()> 0.5):
						bd[(a,b)]='n'
						bd[(a+1,b)]='n'
						bd[(a,b+1)]='s'
						bd[(a+1,b+1)]='s'
					else:
						bd[(a,b)]='w'
						bd[(a+1,b)]='e'
						bd[(a,b+1)]='w'
						bd[(a+1,b+1)]='e'
		self.tile = bd
		return self	
				
	def shuffle(self):
		bd = self.tile
		x = aztecDiamond(bd[0]+1)
		board = x.tile
		n = bd[0]
		for k in range(1,2*n+1):
			l = min(2*k,4*n-2*k+2)
			for j in range(l):
				if(bd[(j+  0.5 - l/2,k-n - 0.5)].lower() == "n"): board[(j+  0.5 - l/2,k-n - 0.5 - 1)] = bd[(j+  0.5 - l/2,k-n - 0.5)]
				if(bd[(j+  0.5 - l/2,k-n - 0.5)].lower() == "e"): board[(j+  0.5 - l/2 + 1,k-n - 0.5)] = bd[(j+  0.5 - l/2,k-n - 0.5)]
				if(bd[(j+  0.5 - l/2,k-n - 0.5)].lower() == "s"): board[(j+  0.5 - l/2,k-n - 0.5 + 1)] = bd[(j+  0.5 - l/2,k-n - 0.5)]
				if(bd[(j+  0.5 - l/2,k-n - 0.5)].lower() == "w"): board[(j+  0.5 - l/2 - 1,k-n - 0.5)] = bd[(j+  0.5 - l/2,k-n - 0.5)]
		return x
	
	def __str__(self):
		bd = self.tile
		n = bd[0]
		s = ''
		for k in range(1,2*n+1):
			l = min(2*k,4*n-2*k+2)
			s +=  ((2*n-l)/2*'.')+ ''.join([bd[(j+  0.5 - l/2,k-n - 0.5)] for j in range(l)])+((2*n-l)/2*'.') + '\n'
		return s.replace('x',' ')
	def toSVG( self, out):
		ADpage = file(out,'w')
		n = self.tile[0]
		ADpage.write('<svg xmlns="http://www.w3.org/dx00/svg" version="1.1">\n')
		w=1
		color='black'
		dx = 10
		for k in range(1,2*n+1):
					l = min(2*k,4*n-2*k+2)
					c = 0
					for x in ['.' for j in range((2*n-l)/2)] + [self.tile[(j+  0.5 - l/2,k-n - 0.5)] for j in range(l)]+['.' for j in range((2*n-l)/2)]:
						if(x=='e'):
							ADpage.write('<rect width="%s" height = "%s" x="%s" y="%s" style="fill:#3366FF" />\n' %(dx,dx,c,dx*k))
						if(x=='w'):
							ADpage.write('<rect width="%s" height = "%s" x="%s" y="%s" style="fill:orange" />\n' %(dx,dx,c,dx*k))
						if(x=='n'):
							ADpage.write('<rect width="%s" height = "%s" x="%s" y="%s" style="fill:greenyellow" />\n' %(dx,dx,c,dx*k))
						if(x=='s'):
							ADpage.write('<rect width="%s" height = "%s" x="%s" y="%s" style="fill:#CC0000" />\n' %(dx,dx,c,dx*k))
						c += dx
		ADpage.write('</svg>')
if __name__== '__main__':
	bd = aztecDiamond('nn\nss')
	#bd = aztecDiamond(file('in.txt').read())

	m = input('Aztec Diamond size? ')
	for x in range(m-1):
		bd = bd.removeBadBlocks().shuffle().fillGoodBlocks()
	print str(bd)
	bd.toSVG('out.html')A

gistfile1.md