fractalize

This page plays with a question of Noam Zeilberger. This is not exactly what Noam wants, i.e. to find a lambda calculus way to generate a sequence of graphs (of lambda terms) as the result of his transformations tau and taubar prop. 4.2 in this article.

The question I like to pose is: can we "fractalize" graphs in chemlambda v2 by replacing each node L with a triple L-L-A and each node A with a triple A-A-L, in such a way that if the initial graph corresponds to a lambda term then the fractalized graph is still one corresponding to a lambda term? The fractalized graph should then reduce as the initial one, eventually.

Partially we can, by geometrically warping the β rewrite, but for the moment not in a way compatible with lambda calculus. Moreover, because chemlambda has two mechanisms of duplication, which may be too much sometimes, the fractalized graph does not always randomly reduce to the initial one, eventually, even if we modify the rewrites A-FO, A-FOE and we inhibit the FO-FOE rewrites, as illustrated in hapax here and as suggested by ishanpm who wrote the javascript version of chemlambda v2 with this alternate set of rewrites as well (except that I had to inhibit FO-FOE).

USE: 1) choose a graph from the list, 2) choose a number of fractal steps, 3) if you want to use alternate rewrites, click that button, 4) click on fractalize button, 5) mouse hover over nodes or click on ">" to start and on "||" to stop.