Tao’s patterns continued
Tao and I discussed a way to describe simple patterns that I presented in a previous post. We assign one out of two colors to 16 cells in a 4 x 4 square using a serie of sixteen 0 and 1, 1010101010101010 for example could be rendered like this:
A few weeks ago I was reading about the notation system that Turing used to describes programs in his 1936 paper and awkwardly it made me think that our much more modest system has two interesting properties: it describes a finite set of patterns and they can be ordered. From there I thought that it would be easy to find a way to calculate all the possible patterns that our notation system can describe: it is the set of all integers between 0 and 1111111111111111 that only contains the numbers 0 and 1. The following python function returns a list of all theses patterns:
def all_patterns():
l = [0,1]
i = 1
while i <= pow(10,14):
i = i*10
[l.append(i+e) for e in copy(l)]
return l
The result in a text file all_patterns.txt. I used the code above in a very nice python graphics application called Nodebox to generate a 1024 x 1024 pixels image of all the possible 4 x 4 cells patterns, from left to right, top to bottom, ordered from the smaller integer (an all white cells pattern) to the biggest (an all black cells pattern):
all_patterns.pdf [PDF file — 1,7 MB]
generate_all_patterns.zip [nodebox code]
I love to zoom in and out in the result and navigate in it, I love to think as well that this image could be used as many things: a coloring poster, a background for a grotesque Shintaro Kago manga, a board for a strange board game…
Some screenshots:
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(Via pierre.archives.)
Pierre: I could not resist to post it! I love this really much!
April 2nd, 2008 at 11:53 pm
hey, super! thank you… I’m happy that you liked this project.