The Evolution of BrainPaint and Fractal Images

In 1975 a mathematician, Benoît B. Mandelbrot, coined the term “fractal” and is best known as the "father of fractal geometry".

Benoit used a computer to plot images of fractals called Julia sets from the formula z² - μ, which was based on the previous work by Gaston Julia and Pierre Fatou.

He emphasized the use of fractals as realistic and useful models of many phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structure of plants, blood vessels and lungs; the clustering of galaxies. Man-made fractals include stock market prices but also music, painting and architecture. Far from being unnatural, Mandelbrot held the view that fractals were, in many ways, more intuitive and natural than the artificially smooth objects of traditional geometry.

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

– B.Mandelbrot, introduction to The Fractal Geometry of Nature

This last quote best illustrates Bill Scott’s motivation to find a medium that could be used to deliver feedback on the complexity of a person’s EEG. Up until BrainPaint, most neurofeedback systems used linear games such as those reminiscent of the 1980s. These games only provide feedback on the linear components of the EEG – frequency (pitch) and amplitude (volume). This is akin to using a cone to illustrate a mountain. Bill wanted to provide his clients with feedback on all the textures and information from their brainwaves.

There was another observation that had been gnawing at Bill. When he analyzed data from his colleagues and his own research on amplitude and frequency data, he found insignificant changes in these variables, even after there were noteworthy and predictable improvements in brain function as measured by fMRIs, response time to light or sound, and improvements in continuous performance tests. On the occasions when the slower frequencies of delta, theta and alpha were abnormally high or low they did appear to regress to the mean, however, it bore no direct relationship to training direction. Bill postulates that when the brain is given feedback about its states using amplitude and frequency the brain in turn extracts information about the complex shapes of these waveforms in order to develop improved control. It was as if when the brain is fed information using only consonants it figures out the meaning by interpolating the missing vowels. What if we gave feedback to the brain using consonants and vowels along with punctuation?

Since games are linear in nature, Bill could not use these traditional methods for providing information on the complex nature of the brain. Therefore, he chose fractals – mathematical graphs or visual representations of chaos theory. After all, the brain is a complex system. Bill needed to couple fractal images with our neurophysiology in order to provide non-linear feedback on the non-linear aspects of our brainwaves.

Bill first used Fractint to generate his early mathematical formulas, which allowed him to explore the fractal dimensions of the EEG. This program proved to be too slow for the animation needed during an EEG biofeedback session.

Scott Draves then created the Fractal Flame algorithm, which was innovative in that it mapped out the non-linear functions of fractals, in addition to, the log-density display and structural coloring. This algorithm exposed and preserved much more information than previous incarnations of fractal generators.

Then Mark Townsend created Apophysis, which made Draves’ Fractal Flame more user-friendly allowing users to create static images that are manually manipulated to created new static images.

Bill watched all these advancements in fractal technology; however, he was still far away from a vision he had of his dream EEG biofeedback system. He had one obstacle left and began developing his own software that would allow brainwaves to dynamically manipulate elements. If we go back to our earlier analogy, Scott Draves took a snapshot of the ocean and then Bill added the wind, gravity, currents and forces that move the tide. The nature of complex systems is that they are infinitely sensitive to influence, and this is what Bill needed to capture. It is this life force that makes up the power of our brain, and Bill married these neurological influences to a mathematical universe.

BrainPaint has stayed true to traditional forms of neurofeedback incorporating a game derived from the linear variables of amplitude and frequency. Layered upon this already proven delivery system, BrainPaint has added feedback on non-linear data extracted from the morphology of the EEG. This feedback is represented in the beautiful fractal images. UCLA Professor Lobsang Rapgay is currently conducting a study on the efficacy of the BrainPaint system as compared to tradition neurofeedback for ADHD symptoms.

"I wonder whether fractal images are not touching the very structure of our brains. Is there a clue in the infinitely regressing character of such images that illuminates our perception of art? Could it be that a fractal image is of such extraordinary richness, it is bound to resonate with our neuronal circuits and stimulate the pleasure I infer we all feel."

– Professor Peter W. Atkins, Lincoln College, Oxford University, “Art as Science,” The Daily Telegraph