Animating the Quantum Drunkard’s Walk

A recent PPCG challenge titled The Quantum Drunkard’s Walk was about a tiny drunken person for which quantum mechanics apply and who — being drunk — will randomly walk in one of the four cardinal directions each step they take.
As they experience the strange world of quanta, they can simultaneously take every path at once and their paths influence each other. The challenge then asked to output all possible positions the quantum drunkard could occupy, all paths they could take in ASCII representation.

The question also states this problem’s equivalence to a cellular automaton, when one removes the story boilerplate.
Cells in this cellular automaton are square and can occupy one of three states: empty, awake or sleeping. Each iteration, all cells change according to three rules.

  • An empty cell wakes up iff there is exactly one awake cell amongst its cardinal neighbours, else it stays empty.
  • An awake cell goes to sleep.
  • A sleeping cell continues to sleep.

Being code golf, the aim was to come up with a minimally sized source code; my attempt required 214 bytes and prints a nested array containing one-length strings (characters), as this output method is cheaper than concatenating all characters to one string.

python quantum.py -rmi 200
python quantum.py -rmi 200

However, one user took the challenge idea a bit further and created an animated gif showing the walk’s, or cellular automaton’s, progression over time with an increasing number of iterations. My Python program shown in this post does exactly that, generating an animated gif showing the automaton’s progression. I even implemented rainbow support, possibly improving the automaton’s visual appearance.
Python source code can be downloaded and seen below.

I use the Python Imaging Library to produce all frames and use a shell call to let ImageMagick convert all frames to an animated gif. Animation parameters are taken via shell arguments, a full list of features follows (also available via the -h flag).

  • --iterations N Number of iterations (initial frame not counted)
  • --colorempty C Empty cell color (#rrggbb)
  • --colorawake C Awake cell color (#rrggbb)
  • --colorsleeping C Sleeping cell color (#rrggbb)
  • --rainbow Use rainbow colors (overrides color settings)
  • --scale N Cell square pixel size
  • --convert Execute ImageMagick’s convert command
  • --delay N Delay between frames in output image.
  • --loop N Gif loops (0 means for indefinite looping)
  • --keepfiles Do not delete files when converting
python quantum.py -s 25 -md 50
python quantum.py -s 25 -md 50

# Python 2.7 code; Jonathan Frech; 1st of December 2017

# All cells can either be empty (0), awake (1) or sleeping (2). In each step:
# * empty -> awake iff cell adjacent to exactly one awake, else empty
# * awake -> sleeping
# * sleeping -> sleeping

# import
import argparse, sys, time, os

# convert a given hsl color intor rgb
def hsl(h, s, l):
	# value range
	h = h%360
	if not (0<=h<360 and 0<=s<=1  and 0<=l<=1): return
	
	c = (1-abs(2*l-1))*s
	hh = h/60.
	x = c*(1-abs(hh%2-1))
	r = g = b = 0
	if 0 <= hh < 1: r, g = c, x
	if 1 <= hh < 2: r, g = x, c
	if 2 <= hh < 3: g, b = c, x
	if 3 <= hh < 4: g, b = x, c
	if 4 <= hh < 5: r, b = x, c
	if 5 <= hh < 6: r, b = c, x
	m = l-c/2.
	return int((r+m)*255.), int((g+m)*255.), int((b+m)*255.)

# main function
def main():
	# start timer
	t0 = time.time()
	
	# command line parsing
	parser = argparse.ArgumentParser(description = "A specific cellular automaton renderer.")
	parser.add_argument("--iterations"   , "-i", type = int, default = 10       , metavar = "N", help = "Number of iterations (initial frame not counted)")
	parser.add_argument("--colorempty"   , "-b", type = str, default = "#ffffff", metavar = "C", help = "Empty cell color (#rrggbb)"                      )
	parser.add_argument("--colorawake"   , "-c", type = str, default = "#aaaaaa", metavar = "C", help = "Awake cell color (#rrggbb)"                      )
	parser.add_argument("--colorsleeping", "-C", type = str, default = "#000000", metavar = "C", help = "Sleeping cell color (#rrggbb)"                   )
	parser.add_argument("--rainbow"      , "-r", action = "store_true"                         , help = "Use rainbow colors (overrides color settings)"   )
	parser.add_argument("--scale"        , "-s", type = int, default = 1        , metavar = "N", help = "Cell square pixel size"                          )
	parser.add_argument("--convert"      , "-m", action = "store_true"                         , help = "Execute ImageMagick's convert command"           )
	parser.add_argument("--delay"        , "-d", type = int, default = 5        , metavar = "N", help = "Delay between frames in output image."           )
	parser.add_argument("--loop"         , "-l", type = int, default = 0        , metavar = "N", help = "Gif loops (0 means for indefinite looping)"      )
	parser.add_argument("--keepfiles"    , "-k", action = "store_true"                         , help = "Do not delete files when converting"             )
		
	parsed = parser.parse_args()
	# TODO: rainbow
	
	# import error
	try: from PIL import Image
	except ImportError: parser.error("Cannot import Python Imaging Library (PIL).")
	
	# parse a hex color
	def parsecolor(c):
		try:
			if c[0] == "#": c = "0x%s"%c[1:]
			c = int(c, 16); return (c>>16)&0xff, (c>>8)&0xff, c&0xff
		except: return
	
	# argument errors
	if parsed.iterations < 1: parser.error("Minimum number of iterations is 1.")
	parsed.colorempty    = parsecolor(parsed.colorempty   )
	parsed.colorawake    = parsecolor(parsed.colorawake   )
	parsed.colorsleeping = parsecolor(parsed.colorsleeping)
	if not parsed.colorempty   : parser.error("Colorempty is not a valid #rrggbb color."           )
	if not parsed.colorawake   : parser.error("Colorawake cell color is not a valid #rrggbb color.")
	if not parsed.colorsleeping: parser.error("Colorsleeping is not a valid #rrggbb color."        )
	if parsed.scale < 1: parser.error("Minimum scale is 1.")
	if parsed.delay < 1: parser.error("Minimum delay is 1.")
	
	# generate file name from frame number
	def filename(f): return "img%0*d.png" % (len(str(n)), f)
	
	# save frame with matrix A, file name number f
	def saveframe(A, f):
		# create image
		for j, a in enumerate(A): pix[j%s, j/s] = (parsed.colorempty, parsed.colorawake, parsed.colorsleeping)[a]
		
		# scale and save image
		try: img.resize((parsed.scale*s, parsed.scale*s)).save(f); return True
		except: return
	
	# frame number, size, area, matrix, image, pixel array
	n = parsed.iterations
	s = 2*n+1; a = s**2
	A = [0]*a; A[a/2] = 1
	img = Image.new("RGB", (s, s)); pix = img.load()
	
	# main loop
	for f in range(n+1):
		# status message
		sys.stdout.write("\r\33[K[%s] %06.2f%%" % ("-\|/"[f/4%4], 100./n*f)); sys.stdout.flush()
		
		# rainbow feature
		if parsed.rainbow: parsed.colorempty = (0, 0, 0); parsed.colorsleeping = hsl(360./n*f, .5, .5); parsed.colorawake = hsl(360-360./n*f, .5, .5);
		
		# frame has to be saved successfully
		if not saveframe(A, filename(f)): print "\r\33[KFailed to save frame number %d.\nRendering aborted." % f; break
		
		# iterate: 0 -> 1 if surrounding cells contain exactly one 1, else 0; 1 -> 2, 2 -> 2
		A = [{0: 1 if [j%s>0 and A[j-1], j%s<s-1 and A[j+1], j/s>0 and A[j-s], j/s<s-1 and A[j+s]].count(1) == 1 else 0, 1: 2, 2: 2}[a] for j, a in enumerate(A)]

	# rendering has finished
	t1 = time.time()
	print "\r\33[KRendering took %.2f seconds." % (t1-t0)
	
	# converting images to gif
	if parsed.convert:
		print "Calling ImageMagick..."
		try: os.system("convert -delay %d -loop %d img*.png out.gif" % (parsed.delay, parsed.loop))
		except: print "Failed to convert frames to gif."
		else:
			print "Cleaning up..."
			for f in range(n+1): os.remove(filename(f))
			t2 = time.time(); print "Converting took %.2f seconds, finished in %.2f seconds." % (t2-t1, t2-t0)
	
# run if main
if __name__ == "__main__": main()
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One thought on “Animating the Quantum Drunkard’s Walk

  1. Pingback: Third Anniversary – J-Blog

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