The Cook Book
Recipe for the week of April 24  30
Life Without Death (revisited)
 Recall our virtual snowflake from the week of February 13, generated
by the CA rule that we now call Life Without Death: an empty site
becomes occupied if there are exactly 3 occupied sites in its range 1 Box
neighborhood. In other words, this is Conway's Game without the
transitions from occupied to empty. Starting with a radius 50 lattice
ball, the evolution produced a complex pattern reminiscent of ice crystals.
We mentioned at the time that we had no idea whether or not the growth would
continue in all radial directions.
 In an attempt to gain further insight into the remarkably intricate
dynamics of this simple rule, we have conducted a number of additional
Life Without Death experiments starting from large balls. Kellie Evans
grew this week's soup, using WinCA, by starting from a ball of
'radius' 80. In order to capture as large a flake as possible she
appealed to the lattice symmetry and positioned one quarter of the
initial disc at the extreme upper left of the array. Our graphic shows
the result after 6000 updates. We have reduced the image to 1/9 its
original area for easy viewing; those blessed with large desktops and
lots of memory should see the original 1500 by 1300
hugesoup.gif.
 Note the nearly periodic structure extending in the diagonal
directions. Thus there seems to be some preliminary evidence that this
growth is increasingly 'healthy' as time goes on. But the subtlety of the
survival question is indicated by the fact that, even for large radii,
small changes in the size of the initial ball can produce radically
different trajectories. We have not yet attempted a detailed empirical
study of this sensitive dependence on initial conditions to see whether
any quantifiable regularity can be identified. But surely Life Without
Death is one of the very simplest twodimensional CA growth models with
exemplary chaotic dynamics.
