Cousins

I thought Kaya and Bodie were step-siblings. Actually, they are cousins. Kaya came for a visit just now. You can see that we've trimmed Bodie's ears and tail.

Bodie

We have adopted a genetically modified wolf. The horror! It's been six-and-a-half years since we lost Micky, a wheaten terrier. Late June we took in (for a week) our friends' miniature poodle, Kaya, and I guess it rekindled in Catherine some dog-ownership benefits. Six-month-old Bodie (rhymes with Jodie) and Kaya are cousins.

Cracks in the crystal

In the late 1980s, I consumed reams of paper printing out (using my HP 75C) evolutions of elementary cellular automaton rule #193 (which in binary is 11000001, suggesting that the central cells of 111, 110, and 000 remain or become 1 in the next generation). This is the mirrored complement of the more famous rule #110. In rule #193, the ones form right "triangles" with a jagged hypotenuse facing southwest. Back then, in order to conserve ink I suppressed the printing of triangles of size-3 which (in evolutions of random starts) soon predominate. Looking at the time history of an evolution, the staggered size-3 triangles form a sort of "crystal" based on the stable configuration of the following cell (left and right are joined, time moves down):

00000100110111

01110000010011

00110111000001

00010011011100

11000001001101

11011100000100

01001101110000

Yesterday I spent some time programming this old plaything in Mathematica. Here is how a larger configuration of crystal cells appears in my implementation:

The lighter-blue ones of the size-3 triangles are meant to blend in with the darker-blue zeros, providing contrast for the other-sized triangles (in orange) of a typical evolution, out of which I have cropped this small detail:

The orange "particles" are recognized as defects, or cracks, in the crystal. They move left or right or just stand still. Colliding particles obviously conserve the sum of the defect offset numbers that individual particles may be said to possess, as they interact and regroup, or occasionally disappear. You can surmise from the (final) four particles at the very bottom of my example that the size of my space is a multiple of 14, the necessary space-size of a left-right-joined perfect crystal. (The right-moving particles will crash into the left-moving particles and disappear.)