Portraits

Read the chapter submission...
Evolving the Mandelbrot Set to Imitate Figurative Art (PDF)
by JJ Ventrella
to be published as a chapter in the book, Innovations in Evolutionary Design, Natural Computing Series,
Springer-Verlag, Berlin, 2007, edited by Hingston, P., Barone, L., and Michalewicz, Z.

The technique was originally created for La 17 Exposición de Audiovisuales in Bilbao, Basque country, Spain, December, 2004, coordinated by Josu Rekalde of la Universidad del País Vasco. Special thanks to Josu and Agueda Simo for help, inspiration, and friendship.

An artist who has spent his or her formative years with hands in clay, paint and wood might approach mathematics in one of two ways: (1) it is an inaccessible and arcane collection of numbers and symbols to be avoided as irrelevant to artistic expression, or (2) it is a living, breathing, plastic medium, to be coerced into something visually evocative.

The Mandelbrot Set
The Mandelbrot Set was an important discovery (or invention?) A wealth of mathematics, as well as spectacular imagery, has come about in the wake of this discovery. Complex math, and the method for generating the Mandelbrot Set, is largely the preoccupation of trained professionals, and a degree of rigor is required to understand its techniques and implications. However, the core algorithm for generating computer images of the Set are relatively simple, and anyone can write a short software program to create examples of the stunning imagery that has become familiar to us all. But as I see it, the majority of this imagery falls on the level of the retina and never goes deeper. It is a form of eye-candy. The wild exuberance of colored spirals and filigrees might be described as “Psychedelic Baroque”.

As a tool for visual expression, the Mandelbrot equation has not sufficiently been given a good workout – tweaked, molded, deconstructed – using the tools of visual language. Why is this? To embrace the Mandelbrot Set is to fall in love with the simplicity behind its incomprehensible complexity. And in doing so, artists can lose the sense of irreverence that is sometimes necessary to pull something out of context and expand its vocabulary into a new domain.

What is required is enough understanding of the mathematical principles and skill in software programming to put all of that in the background, much the way an experienced pianist is able to focus on the groove, the expressive content, while letting the fingers take care of the low-level mechanics.

Mathematical Epiphany
My initial discovery of fractal geometry resulted in such a mathematical epiphany, pulling me out of the visual language space, and causing me to pontificate on the nature of Numbers, the nature of Nature, and the way complexity comes into being. After the hangover of this intoxicating love-affair, I realized that something deeper than mathematical elegance was to be appreciated – Fractal Geometry tells us something about process. And this process might in fact have something in common with human creativity and art-making. Thus began a journey for me in discovering ways to use this rich medium for visual expression, where the laws of visual language take precedence over the laws of mathematics.

Toward a Genetic Visual Language
As a part of this journey, I had generated a large series of images in the early 90’s of a specific treatment of the Mandelbrot equation, resulting in a variety of organic, gestural forms. My total mutilation of the equation caused a mathematician who specialized in the Set to disregard my explorations as completely outside of any legitimate analysis from the standpoint of Complex Analysis. I took this as a sign that I was on the right track, and continued to mutilate the equation, exposing more and more parameters that enabled visual treatment, each parameter representing an adjective – a descriptor – of some visual concept.

Repeated visual assessment was required to arrive at sets of parameters which resulted in effective imagery. These parameters began to take on the metaphor of genetics, due to the infinite varieties of organic forms that resulted from their manipulations.

But more importantly, the generation of imagery in the visual field was completely “hands-off”. I had chosen not to apply any visual manipulation to the images directly (for example, using a brush in Photoshop) but rather to grow all of the imagery by way of adjusting parameters and then re-mapping the equation to evaluate the resulting image, often hundreds of times, until satisfied. Like real-world genetics, the “genotype” (the parameters of the equation) and the “phenotype” (the resulting imagery) are distinct and separate.

Portraiture
In the years since making this series, I had developed some animated works using genetic algorithms, and wanted to apply genetic algorithms to this method of image-making, but never could come up with a good example of a Darwinian “fitness value” to guide the evolution of imagery. But then an idea came up. Having worked as a portrait artist at an amusement park, then later having developed a genetic representation for designing virtual humans, I decided to apply these experiences to the Mandelbrot equation.

And so I revived the software program and applied an evolutionary component. In this new program, a population of hundreds of images evolves through many thousands of matings and deaths to take on a similarity to a digital photograph of my face. This is done by comparing pixel-to-pixel the color values of each image with the original digitized photograph. After a considerable degree of evolution, the image with the highest “fitness” is then chosen out of that population, and re-mapped in higher-resolution, using the evolved genotype.

Visual References
The influence of the paintings of Francis Bacon on my visual vocabulary became apparent to me as I picked among the various evolved portraits from this new series. Other influences may be present as well in these choices. But this is not as interesting to me as the references that may be invoked in others while looking at these images. While they are not entirely face-like, there is still a sense that these images are trying to imitate “something”. This intentionality comes out in these images and perhaps points to other experiences in our visual lives.

The fact that the Mandelbrot equation is the original engine – even with such a strong departure from its pure form – might be the reason so much else emerges in these images, besides the form of a face. For the final selection process, I have chosen the images that contain visual references that have meaning to me. And this is the reason why I consider them to be self-portraits.