Escherized metapixel

[metaweta]

The OTCA metapixel is a 2048 x 2048 life pattern that simulates the life rules, life-in-life. It runs with a period of approximately 2^15. The machinery of the pattern is around the edge of the square; the center is a vast field that gets flooded with LWSSs when the cell is in the ON state. Golly (free software for running cellular automata) provides a "metafier" script that takes the current selection and re-renders it using metapixels.

I took a single row of LWSSs so that by starting at Golly's maximum magnification I could double the resolution 11 times and end up "where I started". This gave an image that is periodic both in theta and in log(r). By taking the complex log of the image, I got a rectangular tiling of the plane. I then rotated and scaled that tiling, getting a new tiling that still had 2pi periodicity in theta, and then exponentiated it. This is the same conformal transformation that Escher intuited in his "Print Gallery":
http://images.google.com/images?q=escher+print+gallery

You can find the metapixel images in two posts on my blog:
http://reperiendi.wordpress.com/2011/03 ... metapixel/
http://reperiendi.wordpress.com/2011/03 ... metapixel/

[p46beth]

Could you give the .rle or .mc file for the pattern? You can get it from golly simply by copying and pasting a pattern into your post

[Joel]

Could you give the .rle or .mc file for the pattern? You can get it from golly simply by copying and pasting a pattern into your post

I think that a life pattern that simulates life is going to be huge! By the way, correct me if I am mistaken, but I believe I saw something similar to this in the Golly sample patterns.

[metaweta]

As Joel said, it would be huge: each metapixel is 2048x2048, and there were around 85x15 of those. But it's trivial to generate the pattern:
1) select a single "on" pixel, and use the metafier script.
2) zoom into the center and select a few LWSSs, then use the metafier script again.