IceNine

This article is about a hypothetical unstoppable quadratic growth pattern. For a Life-like rule, see OCA:Iceballs.

IceNine is Dave Greene's name for a hypothetical unstoppable quadratic growth pattern that expands outward through random ash at speed c/137, described as follows in a tongue-in-cheek post in February 2008:

“ Aha! You and your intuition have clearly not been exposed to the IceNine Agar, found recently with an alternate-universe oscilloscope:

#C IceNine seed -- currently this is the smallest sample
#C for which no external conditions have yet been found
#C that prevent long-term quadratic growth
x = 2718, y = 4669, rule = B3/S23
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Every sufficiently large and ancient B3/S23 universe observed so far turns out to be full of this weird agar, which expands in all directions through random ash at c/137. IceNine seems to absorb blocks and blinkers particularly well, due to a complicated froth of sparks at its front lines -- not generated by glider collisions, but by a lucky accident of the agar's internal structure.

When the expanding front touches an active pattern that it can't immediately annihilate, the pattern "dies back" a short distance at near lightspeed, leaving behind a protective scattering of blocks; behind the blocks the front stabilizes and starts expanding again. Converging IceNine fronts usually cause small diebacks that stabilize as small defects in an apparent quasicrystalline structure.

And before you all ask, my alternate-universe oscilloscope was repossessed by the Outsiders the other day, so unfortunately I can't lend it out. But there didn't seem to be anything but IceNine out there anyway --

”

He went on to further characterize IceNine as follows:

“ The IceNine I tried to describe doesn't have a memory per se, any more than a cell's DNA knows the position of every lipid molecule in its cell wall. It's an active, growing agar with lots of edge sparks that just happen to annihilate nearby gliders and still lifes unusually efficiently. Along with several other utterly improbable properties. Basically it's the spacefiller that wins the Survival of the Fittest Award in an infinite Life universe, and it's about as likely as the proverbial tornado in a junkyard building a jumbo jet. ”

It is generally agreed that a pattern exhibiting the characteristics of IceNine cannot exist in Conway's Game of Life, but a formal proof remains elusive. However, mechanisms that a replicator could implement to clear random ash fields with a similar "dying back" process to the one described by Greene to act as a failsafe have been proposed and have been demonstrated to work with greater than 50% odds of success.

Notes

The coefficient 1/137 is likely a reference to the fine-structure constant , a physical constant independent on the system of units in which it is measured. It was thought to be exactly 1/137, but more accurate measurements have found its denominator to be more precisely 137.035999206. (See  A005600.)</ref>

The dimensions x = 2718 and y = 4669 of the omitted RLE file are likely references to Euler's number and Feigenbaum's constant respectively, being the first four digits of each constant.

External links

• Adam P. Goucher (June 13, 2009). Re: Stable Life? (discussion thread) at the ConwayLife.com forums