# Definition of geometric space around analytic fractal trees using derivative coordinate funtions

## TL;DR

This paper introduces a new geometric framework around analytic fractal trees using derivative coordinate functions, extending the concept from 2D to higher dimensions and discussing potential applications.

## Contribution

It defines a novel fractal space geometry around analytic fractal trees and extends it to R3 and Rn, enhancing the mathematical understanding of fractal structures.

## Key findings

- Defined canonical and degenerate forms of fractal space
- Extended fractal geometry to three and higher dimensions
- Discussed potential applications of the new fractal geometry

## Abstract

The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space around these fractal trees. We present the canonical and degenerate form of this fractal space and extend the fractal geometrical space to R3 specifically and Rn by a recurrence relation. We also discuss the usage of such fractal geometry.