Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

27 April 2007

Hex Counter and Cells Within Cells

Some incredible patterns have been included with the latest version of Golly, a cross-platform editor and player that can display huge CA patterns, and often run them at unheard-of speeds. Golly 1.2 came out in mid-April on SourceForge; one of the new patterns is a two-digit hexadecimal counter implemented as a Conway's Life pattern. It's a modernization of sorts of Alan Hensel's 1994 "Decimal Counter" pattern -- an animated Java version of which is now available on the Web [collidoscope.com].

Another set of patterns by the same author, using some of the same components, are composed of huge grids of metapixels -- regions thousands of cells square that are designed to mimic the behavior of the underlying cellular automaton, or that can be "reprogrammed" to simulate other rules.

The Golly engine is based on hashlife (see the Dr. Dobb's Journal link for details on how the algorithm works).

The hex counter can be found in the Hashing-Examples folder in Golly's pattern collection, along with three metapixel samples. This series of screenshots shows the counter in action at various scales.

The first screenshot shows individual cells in the underlying grid, making up two still lifes (a block and a fishhook eater) and two spaceships (lightweight and middleweight).

The two spaceships are part of a high-period salvo that either creates a block or 'pulls' it along a row of memory bits that encode each pixel of the 'hex counter' movie.

The two blockers in the lower left corner both suppress the creation of blocks. The one on the left ends the block-pull cycle and allows the movie to cycle back to the beginning. The one on the right cleans up the extra block in an identical reaction triggered by the salvo-suppression glider coming in from the upper left, instead of by a block.

The suppressing glider is itself suppressed by a glider from a high-period Herschel-based gun that ends just to the right of this image. It is made from a long series of Herschel period-doublers plus a Herschel-to-glider converter.

This is the first subpixel zoom in the series, so individual cells can no longer be seen and shapes may become somewhat distorted. For example, the two seven-bit eaters at center left, which are part of the row of 'memory bits' that tell the movie pixel when to toggle ON and OFF, are reduced to four-bit polyominoes in this view.

The rows of lightweight spaceships (LWSSs) that form the ON state of each movie pixel can now be seen clearly at the top. No LWSSs can be seen at the bottom edge because that pixel is currently turned OFF.

Here an entire edge of a single movie metapixel can be seen; in the center can be seen the row of memory bits that encode half of the metapixel's contribution to the movie. For compactness, the even and odd bits of the movie are stored along separate edges of the metapixels.

The other half of the movie's frames are encoded in a column along the left edge of the movie metapixel, on a diagonal mirror-image from the row along the bottom. At this zoom, two entire metapixels are visible, and the memory-bit columns are visible only as thin vertical lines at the far left. It can be seen that different metapixels contain different coded sequences.

Here several metapixels can be seen at once. The differential shading between the two halves of the pixels at this scale is an artifact of the LWSSs' rectangular shape, and the fact that they are not spaced a power-of-two distance from each other.

At this scale the pixels appear solid and almost all of the details of the control mechanisms are too small to be seen.

At this scale the entire 'movie screen' can be seen. The movie's frame rate will vary widely depending on the memory and CPU speed, but with a step size of 8^4 or 8^5 it may reach several frames per second once Golly's hash tables have been populated.

A final view of the movie screen with all the construction details lost in the distance.