# Nick Mendler

Student of mathematics

University of San Francisco

San Francisco

The artwork below consists of explorations within a family of fractals that have been engineered to exhibit a specific type of connectedness. All fractals are limits, or "canopies" of symmetric binary trees. These trees are defined by two parameters, one that denotes half the angle measure of the spread between branches and a second that sets the ratio between the successive branches. It's possible to narrow this to a one dimensional parameter space by finding a bijection between the angle and ratio parameters that would also force favorable behavior in the canopies. The result has been a fascinating set of fractal curves whose features develop continuously through a wide range of structures.

Woven

20 x 32 cm

Digital Print

2016

While working towards a goal involving connectedness for canopy sets generated with angle and ratio parameters; I found that the domain of possible angles is partitioned into infinitely many sub-intervals. Each interval having a unique formula for the relationship between parameters for the desired behavior. 'Woven' presents one such region, simultaneously drawing all fractals with their angle parameter in the interval [3pi/4 , pi/2). This interval is remarkable because it lies between the the only two space filling curves that occur in the set, namely an isosceles right triangle and a golden rectangle, seen in the foreground and fading out in the background respectively.

Cardiod Eddies

30 x 30 cm

Digital Print

2016

The emergent cardioid illustrates the evolution of a specific fractal curve across the entire domain of an angle parameter while a ratio parameter is fixed at 0.618. Selected for its beauty and unexpected contrast with the component fractal curves, 'Cardioid Eddies' shows the smooth dynamic underlying the progression of the sharp and angular canopies.