List of Generations rules

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The following is a list of Generations rules.

Rule (B/S/C) Rule (S/B/C equivalent) Name Character Author Date
B3457/S2367/C5 2367/3457/5 Banners Exploding Mirek Wójtowicz
A rule that often produces spaceships with growing fluttering banners.
B23/S23/C8 23/23/8 BelZhab Exploding ?
A rule exhibiting Zhabotinsky reactions.
B23/S145678/C8 145678/23/8 BelZhab Sediment Exploding Jason Rampe
The rule creates BelZhab-like patterns that have growing regions of "sedimentary deposits".
B34678/S234/C24 234/34678/24 Bloomerang Expanding John Elliott July 2000
A wave rule that rebounds into a kinder, gentler form of kaleidoscopics — rounded, soft, full, and slow.
B24/S345/C25 345/24/25 Bombers Chaotic Mirek Wójtowicz
A close variant of the Star Wars rule with many more history steps, resulting in beautiful ships, puffers and oscillators.
B246/S6/C3 6/246/3 Brain 6 Chaotic Michael Sweney
An interesting variation of the immortal Brian's Brain, with many patterns constructed.
B2/S/C3 /2/3 Brian's Brain Chaotic Brian Silverman
Also called BB, or simply Brain, this is unquestionably one of the best known and most beautiful CA rules. If we name the possible cell values based on a simplistic neural analogy, viz. 0 = "ready", 1 = "firing", 2 = "refractory", then this simple rule can be stated thusly: Only a cell in the ready state may fire and it will only do so if exactly 2 of its neighbors are firing. After firing for one step, a cell spends a step in the refractory state before regaining readiness.

Although the rule is relatively old, it has never been systematically explored. The rule is so lively that it's not easy to construct stable patterns in it. In December 1999, Michael Sweney discovered the first BB oscillators.

B3468/0235678/C9 0235678/3468/9 Burst Chaotic Michael Sweney
A rule related to Nova, Prairie Fire and others which features large areas of cells that slowly die out or decay into oscillators. Named after a characteristic exploding oscillator. Similar to Day & Night in that constructions can be built both with inside and outside oscillations and growth/decay. Has still lifes similar to Conway Life.
B3468/S235678/C9 235678/3468/9 Burst II Chaotic Michael Sweney
This rule is basically Burst without the single cell still life. It supports slow and fast spaceships, oscillators, and methuselahs as well as a very characteristic p500+ oscillator.
B378/S124567/C4 124567/378/4 Caterpillars Chaotic Mirek Wójtowicz
Named after its very common caterpillar-like patterns.
B24567/05678/C6 05678/24567/6 Chenille Exploding ?
B1234/S2345/C8 2345/1234/8 Circuit Genesis Expanding Charles A. Rockafellor
Circuitry which evolves far beyond its programming and continues to do so long after the initial intput have taken the borders elsewhere.
B2/S23/C8 23/2/8 Cooties Exploding Rudy Rucker
A very vivacious rule, with cells crawling around like mad lice.
B36/S012478/C18 012478/36/18 Ebb and Flow Exploding Michael Sweney
A slow exploding rule with interesting internal dynamics within the growth boundaries. Different types of symmetries will often determine whether a pattern grows indefinitely or dies out. Presents challenging engineering problems. Best viewed in MCell with the standard color palette at speeds of 10 or slower.
B37/S012468/C18 012468/37/18 Ebb and Flow II Exploding Michael Sweney
A close variant of Ebb and Flow that supports simple gliders.
B2/S2/C25 2/2/25 Faders Exploding Rudy Rucker and John Walker
A "genetic" cross of Life and Brian's Brain. A dead Faders cell requires exactly 2 firing neighbors to get turned on. A firing Faders cell keeps firing if it has exactly 2 firing neighbors. And when a Faders cell leaves the firing state it goes into a sequence of refractory states.
B13/S2/C21 2/13/21 Fireworks Exploding John Elliott
Nearly perfect fireworks simulation. It produces interesting results from both random and prepared initial states. Even several cells scattered over the lattice will produce long-running ravishing pictures.
B23/S347/C8 347/23/8 Flaming Starbows Exploding Charles A. Rockafellor
In this world beautiful expanding diamonds and oddly off-parallelograms sweep across the screen leaving trails of fire and spirals of autogenesis. Reminiscent of a mutant spawn of Faders and mad Zhabotinsky spirals.
B34/S12/C3 12/34/3 Frogs Chaotic Scott Robert Ladd
A rule named after its very common frog-like gliders.
B23/S356/C6 356/23/6 Frozen Spirals Cyclic Mirek Wójtowicz
This rule features a popular Zhabotinsky reaction, but with one difference — spirals have icicles in their vertices.
B245678/S035678/C7 035678/245678/7 Glisserati Exploding John Elliott May 2000
"From simple seeds this rule is often highly glideriferous, generating striking kaleidoscopic patterns. Sometimes, though, as in the Glidathon orbit, it is more sparse, in the vein of rules such as Transers, but with much longer transients, providing an uncanny sense of "perpetual motion".

Since I found this rule I've become aware of other recently discovered kaleidoscopic glider rules, such as Snake and TransersII, which share many of the same objects, though I've yet to see a Glidathon style orbit in them (which doesn't mean they aren't there - no one's really looked, AFAIK). In the present version of Glisserati, orbits seeded randomly, as opposed to simply, collapse almost immediately, but that's not the case with the C=5 variation, which is very delicately poised between expansion and contraction. So I've spun that one off as 'Glissergy'." — John Elliott

B245678/035678/C5 035678/245678/5 Glissergy Exploding John Elliott May 2000
"This rule differs from Glisserati only in its cellsize (5 rather than 7). As would be expected, this change is an activity booster - so much so, that, unlike Glisserati, this rule has long transients from random as well as simple starts. Think of it as the pin-iferous answer to Brian's Brain." — John Elliott
B45678/S12345/C8 12345/45678/8 Lava Expanding Mirek Wójtowicz
All patterns are getting very slowly filled with hot lava.
B458/S012345/C3 012345/458/3 Lines Stable Anders Starmark September 2000
This rule quickly self-organizes into linear structures, with separate orthogonally hatched areas. To see the most interesting behaviour, seed the universe with a circle with r≥40 and a density of 20%.
B3/S345/C6 345/3/6 Living On The Edge Chaotic Mirek Wójtowicz February 2000
Also known as LOTE. In this very chaotic rule, it is hard to tell if patterns will survive or die out.
B3/S01245678/C8 01245678/3/8 Meteor Guns Expanding Charles A. Rockafellor
Almost any design above a certain level of complexity results in a slowly exploding ball of fire which then spits fairly large numbers of generational gliders, the titular "meteors". There are easily discovered stable oscillators and static patterns. A truly satisfying environment (if only finding a limited growth meteor gun were as easy...).
B2478/S45678/C25 45678/2478/25 Nova Expanding Mirek Wójtowicz
Very lovely rule characterized by vibrant yet stately streaming growth from solid seeds. The growth patterns and active border have a fascinating geometry, the particulars of which are sensitive to the size and shape of the initial solid.
B2/S3/C4 3/2/4 OrthoGo Exploding John Elliott December 1999
This simple rule supports spontaneous orthogonally productive "glider colliders". But otherwise it seems fairly quiescent.
B34/S345/C6 345/34/6 Prairie on fire Exploding Mirek Wójtowicz
This rule covers the lattice with fire. For best results use yellow-red cells color settings.
B23/S2/C8 2/23/8 RainZha Exploding Rudy Rucker and John Walker
The simplest "Zhabotinsky" style cellular automaton. It spontaneously generates spirals from an initial random pattern.
B2678/S3467/C6 3467/2678/6 Rake Exploding Brian Prentice
This rule is a simple variation of the Worms rule and is characterized by the numerous rake puffers that it generates. Together with the puffers, it generates many ships and expanding wings. These elements can easily be arranged to collide and form ships and puffers of arbitrary complexity.
B25678/S45678/C4 45678/25678/4 SediMental Exploding John Elliott
From a random seed state of 30% ones, the rule tends to form stable "islands", with active coastlines and fascinating inter-island "commerce". But an orbit's fate is quite sensitive to the starting percentage. Below 25% or so the world remains sparsely Brain-like, whereas somewhere above 30% the islands begin to accrete into larger "landmasses", so that by 40% you nearly always end up with a single huge "continent". As for simple seeds, they often lead to surprising results. And the rule clearly has great potential from the "engineering" standpoint.
B25/S03467/C6 03467/25/6 Snake Exploding Brian Prentice
This rule is a simple variation of the Worms rule. It contains two interesting oscillators, a 3*3 square and a shuttle, among its basic elements. By combining copies of the square, many beautiful oscillators can be generated. The rule also generates many puffers one of which generates a sequence of shuttles. The tail generated by the shuttle puffer resembles a snake.
B38/S13458/C6 13458/38/6 Soft Freeze Chaotic John Elliott
"The rule is delicately poised between "solid" and "liquid" phases. From many simple seeds it forms "living crystals" - the crystals form, melt, and reform seemingly indefinitely, in balance with an active phase. The areas of melting can shrink to a point where you're sure everything will freeze over, and then they stage a comeback.

From random starts, this rule resembles a nice poised rule from Wójtowicz called "Living on the Edge", only this one is even more "on the edge". (BTW, though the rule definition looks as though I took LOTE as a starting point, I actually came at it from a different direction entirely, and only afterwards realized I had converged on the B3S345 core.)" — John Elliott

B234/S2/C5 2/234/5 Spirals Exploding ?
The rule produces beautiful stable spirals that unroll forever.
B2/S345/C4 345/2/4 Star Wars Exploding Mirek Wójtowicz March 1999
Also known as MirekGro, this is a very interesting and beautiful rule producing deep space battle scenes; a paradise for patterns' creators in the tradition of Conway Life. It's a successful combination of famous Brian's Brain with a stabilizing factor.

"StarWars is also an interesting rule from the low-investment standpoint. In particular, it is notable for the abundance, intricacy, and variety of its naturally-occurring glider guns. In general when running "au naturel" StarWars is active to a degree almost reminiscent of Brain, with the distinction that it likes to build fixed lego-like skeletal structures. In some orbits this latter penchant reaches its zenith, and we get large universe-spanning "shells" possessing an intricate radiate geometry." — John Elliott

B2/S3456/C6 3456/2/6 Sticks Exploding Rudy Rucker
This interesting rule builds a variety of sticks, with ships floating among them.
B34/S23/C8 23/34/8 Swirl Chaotic Scott Robert Ladd
While spirals are common in CAs (see for example RainZha or Cyclic CAs), Swirl's whirlers are of the rarer discrete variety - isolated "whirlpools" in an otherwise dead sea. There are two sizes of whirlpools that occur regularly. Ladd calls the smaller the "swirlpool" and the larger the "flamewhirl". Also there is a glider with a flickering double tail which Ladd aptly refers to as a fire or flame glider.
B34/S1234/C48 1234/34/48 Thrill Grill Expanding John Elliott July 2000
Sparkling dynamics inhabit and rearrange a grill-like background of one-cells.
B26/S345/C5 345/26/5 Transers Exploding John Elliott
A beautiful and dynamic rule with many distinctive entities that occur "in the wild", with remarkable inter-entity transformations.
B26/S0345/C6 0345/26/6 Transers II Exploding Michael Sweney
B34678/S345/C5 345/34678/5 Wanderers Exploding Mirek Wójtowicz
A rule very similar to "Prairie on fire", but creates interesting dynamically moving patterns.
B25/S3467/C6 3467/25/6 Worms Exploding Mirek Wójtowicz
A very vigorous rule producing crowds of disgusting worms.
B2356/S1456/C16 1456/2356/16 Xtasy Exploding John Elliott July 2000
From simple seeds in a closed universe this is a lovely kaleidoscopic wave rule that tends to do extended meditations on the letter X.