A standard Turing Machine operates on a 1D tape. A "Turmite" extends this into a 2D grid. The read/write head has an orientation (Up, Down, Left, Right) and its transition rules dictate not only the state and character to write, but also the relative turn direction based on the current cell's color.
This simulation deploys multiple independent read/write heads simultaneously onto a shared memory grid. By allowing you to "Mutate Subsets," the simulation models heterogeneous agents executing divergent rule sets, visually demonstrating emergent complexity and concurrent memory access conflicts.
To simulate an infinite tape on a finite screen, the grid utilizes toroidal wrapping. Heads moving off the right edge reappear on the left, ensuring continuous computation without boundary halting states.
Alan Turing proved that no algorithm can determine if every possible program will eventually halt or run forever. The Busy Beaver game plays off this undecidability by asking a specific, finite question that becomes incredibly difficult to answer as states increase.
An N-state Busy Beaver is a Turing Machine that starts on a completely blank tape (all 0s). The goal is to design a state transition table that prints the maximum possible number of 1s before strictly halting. If the machine enters an infinite loop, it is disqualified.
Notice the explosion in complexity. A 2-state machine halts after 6 steps. A 3-state machine halts after 21 steps. A 4-state machine takes 107 steps. The champion for a 5-state machine takes 47,176,870 steps to halt. The value for 6 states is currently unknown, proving how quickly simple finite state machines generate staggering mathematical complexity.