# Placeholder Substructures II: Meta-Fractals, Made of Box-Kites, Fill Infinite-Dimensional Skies

## TL;DR

This paper explores how zero-divisors from hypercomplex numbers, generated via Cayley-Dickson Process, form fractals and scale-free networks as dimensions increase, revealing new meta-fractal structures called 'Skies' built from 'Box-Kites'.

## Contribution

It introduces the concept of meta-fractals or 'Skies' generated from ZDs using Cayley-Dickson Process, and provides simple rules for transforming fractal structures within complex systems.

## Key findings

- Zero-divisors can represent singularities and fractals in infinite dimensions.
- Meta-fractals called 'Skies' are generated for certain integers as strut constants.
- Bit-manipulation rules enable transformation between different fractal structures.

## Abstract

Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any integer greater than 8 and not a power of 2 generates a meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an ensemble of octahedral vertex figures called "Box-Kites" (the fundamental building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes" provide tools for transforming one fractal genus into others within the context of Wolfram's Class 4 complexity.