# Nick Mendler

Student of Mathematics

University of San Francisco

San Francisco California USA

Generative art helps me explore recursion and express the mysterious nature of iterative systems recently made visible by the advent of computers.

In particular, pieces here express the evolution of pairs of fractal trees through selected parameter spaces. Trees are defined by n transformations which specify the self-similarity of an n-branch tree to the n respective copies emanating from an initial trunk segment. Branches are generated by recursively transforming and appending segments in a chain beginning with the trunk, so that the whole tree may be defined as the union of all such chains.

Artwork diverges from the expected appearance of such trees and abstractly views a continuum of parameters all at once through transparency overlay

In particular, pieces here express the evolution of pairs of fractal trees through selected parameter spaces. Trees are defined by n transformations which specify the self-similarity of an n-branch tree to the n respective copies emanating from an initial trunk segment. Branches are generated by recursively transforming and appending segments in a chain beginning with the trunk, so that the whole tree may be defined as the union of all such chains.

Artwork diverges from the expected appearance of such trees and abstractly views a continuum of parameters all at once through transparency overlay

13's Flower

17 x 30 cm

Digital Print

2017

This flower displaying 13 fold symmetry is actually a binary tree whose branches turn at an angle 7 pi / 13 from the trunk while shrinking by a ratio very near to one. The observation that symmetric binary trees with ratios near one displayed n-fold symmetry when given a turning angle that's a rational multiple of pi / n was a landmark in our research. As the branching ratio nears one the tree becomes ultimately unbounded, however a 13-gon appears to manifest around the intricately detailed interior.

Parameter Wind

30 x 20 cm

Digital Print

2017

Here a binary tree is seen in transit between structures as one branch changes in angle and another changes in length.