MAX, the smallest known example of a "spacefiller"
This is the fastest-growing known pattern in Conway's Game of Life
(possibly the fastest possible). It fills space to a density of 1/2,
conjectured to be the maximum density, and does it at a speed of c/2
in each of the 4 directions, which has been proven to be the maximum
Population growth is [(t+19)^2+463]/4 for t divisible by 4;
. [(t+19)^2+487]/4 for t even, not div. by 4;
. [(t+18)^2+639]/4 for t odd.
Original construction, top/bottom stretchers by Hartmut Holzwart;
Size optimization, left/right stretchers by David Bell;
Original idea, middle part, l/r stretcher connection by Al Hensel.
This spacefiller by David Bell, September 1993.
Table of Contents,
About the Applet