Fourier Life Demonstration (click Run or scroll down for blog posts)


Cellular Automata System:   Generation: 0

Even generation rule: B3/S23  Odd generation rule: B2/S56

Tuesday, January 21, 2014

Self-Replicating Creatures

The self-replicating "creatures" come in three varieties (1D, x4 and sp), as indicated in parentheses after each Rule in the drop-down list above. This post describes some of the more interesting "creatures" discovered in the Fourier Life systems explored so far.

1D - Creatures which replicate along a one-dimensional line
  • These are by far the most common type found
  • They can appear as filled cells against an empty background as in Traffic (System B, Rule 15) or empty cells against a filled background as in Nighttime Traffic (System B, Rules 16)
  • Sometimes the 1D creatures compete with others creatures, such as wick-stretchers in Qix! (System C, Rule 4), splitters in Butterflies vs Centipedes (System C, Rule 6) or four-fold replicators in Population Control (System C, Rule 9)
  • The most interesting 1D replicators are ones where the line along which they replicate moves, either diagonally (System C, Rule 9) or horizontal/vertical (System C, Rule 10)

x4 - Creatures have 4-fold symmetry and create four new copies every replication period
  • These are the most common 2-dimensional replicators
  • The copies can sometimes be generated quite far away from the original, such as in Fourth of July (System B, Rule 1) where they are separated by twenty cells!
  • The growth can be continuous as in Raindrops (System B, Rule 5) or can seemingly pause such as in Flowers in Bloom (System B, Rule 3)
  • The replicator can be a continuously moving structure which spawns new copies as it moves outward, such as in Armadillos (System C, Rule 5)
  • This type of replicator usually takes over the world quite easily since it makes four copies each replication period, e.g. Overcrowding (System C, Rule 8), but sometimes other replicators can compete with them, e.g. Population Control (System C, Rule 9).

sp - Creatures split into two (like 1D) but the new copies are rotated 90 degrees from the original so they eventually fill up the whole 2-dimensional world.

  • These are the rarest type and, to me, the most interesting
  • Amazingly enough, the very first self-replicating creature found was also the rarest type (System A, Rule 1)
  • The splitting can appear very deliberate and defined such as in Manta Rays vs Gliders (System B, Rule 2) and Stingrays (System B, Rule 4) or more fluid such as in Shape Shifters (System C, Rule 1) and Rise of the Pheonix (System C, Rule 7). In these latter systems, it is necessary to step through the iterations to actually see how they split in two.
  • Perhaps the most amazing system found so far is Bats on a Checkerboard (System B, Rule 8). These replicators live on a background of an oscillating checker board. The constant flashing is tough to watch so I added a checker-board mask. Once I did this, I realized that there were replicators in each of two different checker board backgrounds which appear light and dark with the mask. There is a semi-stable boundary between the two and keeps the two replicators separated. Over time, one area (either light or dark) eventually takes over the world although sometimes it can take more than a hundred thousand generations.
  • Another variation of "checker-board life" discovered is Bricks on a Checkerboard (System B, Rule 9) but it is difficult to get it started so it's best to run it from Bats on a Checkerboard once the two regions are established.

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