Tick Tock rule definition and introduction
A graph based simple program/complex system which synchronises itself locally.
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.
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.
Notices and Disclaimers
Copyright, under construction, software considerations, related sites.