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A cellular automaton which simulates a Brainfuck interpreter [BSD license]
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Braktif

Braktif is an esoteric programming language very similar to Brainfuck F and Archway, with a small but significant difference: Braktif is formulated as a 28-state cellular automaton.

Braktif playfields are divided into a program on the right and a data storage area on the left. (The data storage area can be considered to extend indefinately to the left.) The program and data area are connected by a "bus". On the bus sit the instruction pointer, which rests underneath the part of the program which is currently executing, and the data pointer, which rests underneath the part of the storage which is currently being addressed. The instruction pointer and data pointer communicate by means of signals (from the IP to the DP) and replies (from the DP to the IP) sent along the bus.

The instructions of a Braktif program resemble those of Smallfuck or Brainfuck F:

*   flip current data bit
>   advance DP one cell to the right
<   advance DP one cell to the left
[   if current data bit == 0, skip to matching ]
]   skip back to matching [

The structure of Braktif programs resembles that of Archway. Each nested loop must be raised up one level. In addition, extra space must be left after [ instructions, and at least one non-[] instruction must occur after a ] instruction, so that signals have sufficient space in which to propagate.

The data storage area of a Braktif playfield resembles the tape of a Brainfuck F program (or a Smallfuck program, if an arbitrary limit is imposed on it) except that it is bounded on the right, not the left.

The final result of all this is that the following Brainfuck F program translates to the following Braktif program (the ... indicates the quiescent repeating pattern extending off to infinity):

Brainfuck F:

+[>+]

Braktif:

                      <*
... 00000000000000 *[---]
... -------------d-i-   --

So... why Braktif?

  • eliminates "spooky action at a distance" from the Brainfuck model: the communication between the code and the tape is made explicit (and explicitly planar, FWIW WRT the wire-crossing problem.)
  • horribly inefficient because of this. Flipping the n'th data cell from the m'th instruction of the program is now an O(n+m) operation. What fun!
  • makes a passable "poor man's visual debugger" for Brainfuck F.
  • makes experimenting with concurrent models easily. For example it might be feasible to add a few states what would act as a simple mutex so that two different programs could share one data store.

Finally, I do not claim that this is the most efficient formulation imaginable... there is certainly room for optimization. For example, half of the Tool states could probably be done away with entirely if the signals were to transition themselves directly into responses. But a minimum of states is not the real goal (otherwise one could just settle for John Conway's Game of Life and be done with it,) and the Tool states lend a certain straightforwardness.

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