cp's OEIS Frontend

The same as A172310 but starting with two L-toothpicks.

We start at stage 0 with no L-toothpicks.

At stage 1 we place two large L-toothpicks in the horizontal direction, as a "X", anywhere in the plane.

At stage 2 we place four small L-toothpicks.

At stage 3 we add eight more large L-toothpicks.

At stage 4 we add eight more small L-toothpicks.

And so on ...

The L-toothpick cellular automaton has an unusual property: the growths in its four wide wedges [North, East, South and West] have a recurrent behavior related to powers of 2, as we can find in other cellular automata (i.e., A212008). On the other hand, in its four narrow wedges [NE, SE, SW, NW] the behavior seems to be chaotic, without any recurrence, similar to the behavior of the snowflake cellular automaton of A161330. The remarkable fact is that with the same rules, different behaviors are produced. (See Applegate's movie version in the Links section.) - Omar E. Pol, Nov 06 2018

The same as A172310 and A172304, but starting from half L-toothpick in the first quadrant.

Note that if n is odd then we add the small L-toothpicks to the structure, otherwise we add the large L-toothpicks to the structure.

We start at stage 0 with half L-toothpick: A segment from (0,0) to (1,1).

At stage 1 we place a small L-toothpick at the exposed toothpick end.

At stage 2 we place two large L-toothpicks.

At stage 3 we place two small L-toothpicks.

At stage 4 we place two large L-toothpicks.

And so on...

The sequence gives the number of L-toothpicks after n stages. A172309 (the first differences) gives the number of L-toothpicks added at the n-th stage.