Tick Tock

Structure and content of website

Tick Tock rule definition and introduction

A graph based simple program/complex system which synchronises itself locally.

Commentary and discussion

The Journey Begins

Potential significance of evolving graphs, discovery of Tick Tock, early results.

Implementation algorithms on a digital computer

Original naive algorithm, conjecture about parentage of higher structure, partly recursive algorithm to exploit conjecture.

Production and evolution of n-simplexes

Central role of simplexes in Tick Tock evolution, mapping n-simplex evolution into n+1 orthogonal dimensions, visualising complex outcomes.

Coordinates reveal boundary hub/joining unit framework

Representing Tick Tock evolution from simplex seeds with orthogonal unit vector coordinates assists recognition of boundary hub/joining unit framework.

Deterministic breaking of symmetry

A detailed look at the origins of the breakdown of symmetry in the first case encountered: the 210 joining units generated from a 6-simplex seed.

Representations of outcomes

Evolution from simple structures

First level emergent mechanisms drive growth from simplex seeds as shown by isolating face joined, edge joined and face edge sharing tetrahedra.

Evolution from a pentatope seed

From t to t+3, a pentatope seed generates five “fully flagged” and fully separated tetrahedra.

3D projection of early 5-simplex inflation

From t to t+3, a 5-simplex seed generates a framework of 30 “hub” tetrahedra each connected to the rest of the framework by 6 of a total of 90 “spokes” which each lengthen exponentially thereafter.

3D projection of early 6-simplex inflation

From t to t+3, a 6-simplex seed generates a framework of 140 “boundary” tetrahedra each connected to the rest of the framework by 6 of a total of 210 “joining units” each of which link 4 boundary hubs.

2D projection of advancing 6-simplex inflation

Snapshots of node density and mimimum other dimension coordinate of an inflaating 6-simplex seed at t+7 projected onto an x, y plane.

Supplementary information

Notices and Disclaimers

Copyright, under construction, software considerations, related sites.