Visualizing the turing tarpit

Abstract

Minimal programming languages like Jot generate limited interest outside of the community of languages enthusiasts. This is unfortunate, because the simplicity of these languages endows them with an inherent beauty and provides deep insight into the nature of computation. We present a way of visualizing the behavior of many Jot programs at once, providing interesting images and also hinting at somewhat non-obvious relationships between programs.In the same way that fractals research has yielded new mathematical insights, research into visualization such as that presented here could produce new perspectives on the structure and nature of computation. A gallery containing the visualizations presented herein can be found at http://tarpit.github.io/ TarpitGazer.

“Viral” Turing Machines, computation from noise and combinatorial hierarchies

“…We first define the IVTM total transition map via an additional technique which is often called "Gödelianization" or "Arithmetization" turning the original table into a list of integers by a change of encoding. The terminology originates in the older Goedel encodings [24], [25] introduced for purposes of theoretical examination of logical proofs and first order logic. Practically, we are interested in all possible ways by which a tuple of n integers can be mapped 1-1 in N as a single integer.…”