Bridges 2025 Exhibition of Mathematical Art, Craft, and Design
Jeffrey Ventrella
Artists
Jeffrey Ventrella
Algorithmic Artist
Petaluma, California, USA
Statement
I am an artist who started falling in love with mathematical ideas early in my career, first by way of geometry and later through the discovery of fractals in the mid-80's. I am a devout Darwinian. I believe that the fundamentals of mathematical language evolved in the biosphere; humans have refined the embodied proto-concepts underlying all biological life to such a degree that we can now simulate the dynamics of evolution, causing mathematical patterns to emerge on their own — echoing a billions-year-long process in a matter of minutes. For me, mathematics is a tool for creativity.
Artworks
This image was generated with the Bubble-Tree algorithm: a single curve motif is grown from a bud at the bottom of the image. The motif is determined by several sine wave parameters. It is scaled and rotated in proportion to the Mother Bubble (the large circle). It gives birth to several buds at internodes. Each bud grows a child bubble that is as large as possible within the confines of the Mother Bubble. Child bubbles determine the coordinate spaces within which new motifs are grown, as new branches. The process continues indefinitely. Bubbles accumulate exponentially. At any given time, only the largest bubble grows a branching motif, insuring that growth cascades from largest to smallest. It is stopped when there is sufficient detail.
This is a space-filling, self-avoiding fractal curve with added visual embellishments to emphasize patterns related to the Koch snowflake. The original fractal curve generator is explained on page 62 of The Family Tree of Fractal Curves:
https://archive.org/details/thefamilytreeoffractalcurves_201907/page/n61