Interview: Melinda Green

Here at Math-Art.net, besides featuring spectacular artwork found in math, or just spectacular art, we also feature artists and mathematicians who are connected with art. We interviewed Melinda Green a few days prior and we’re featuring her as the artist/mathematician this week.

If you had read and subscribed to this site (if you haven’t, you should subscribe right now), you’ll noticed I featured Melinda Green’s discovery, the Buddhagram, a few days ago. And here’s the interview:

Math-Art.net (MA) : Tell us about yourself
Melinda Green (MG) : Well, I’m a 50 year old transsexual (”TS”) woman living in San Francisco with my partner, another TS woman. Obviously the TS thing is a big deal but we’re mostly settled into new lives very nicely. The only connection I can think of between transsexualism and mathematics is that transsexuals may be overrepresented in the field due to our intense desires to understand what’s really going on in the universe. This seems especially true with astronomy which seems to have as deep a connection to pure math than any other science.

I work for Linden Labs as a programmer helping to develop the 3D virtual world called Second Life. My partner is a lawyer for the California judicial system.

MA: You don’t look 50
MG: Thank you! That’s exactly the right thing to say!

MA: Like any mathematical artworks?
My favorite mathematical artist is M.C. Escher. I also love the modern sculptures by George Hart.

MA: Any interests outside work?
MG: I enjoy creating excellent and useful computer user interfaces though I hate wrestling with the computer to achieve that. I enjoy movies, 3D photography, salsa dancing, and combating radio-controlled gliders.

MA: So how did you get into the math field?
MG: My father was a mathematician with a love for sharing interesting mathematical tidbits. I also have an uncle who taught math and who shared lots of interesting puzzles and magic tricks with me. Early on I developed an interest in elegance, geometric forms, and multi-dimensional concepts. For a long time I tried to stay away from my father’s world but I could never shake my love for mathematics which eventually brought me to the sciences.

MA: How did you discover the Buddhabrot?
MG: I was working as a graphics programmer at the time at Autodesk and had become an expert in visualization techniques. I was so intrigued by the simplicity of the description of the Mandelbrot set that, like so many others, I coded up my own rendering software. The beauty and complexity of the forms that it generated were fascinating to me. I started to casually wonder about the mathematical object behind the pictures and wondered whether there might be other natural ways to visualize the m-set. I imagined all of the points in the complex plane iterating at the same time in a big cloud and wondered which regions of that space would be the most popular. That question clearly had an answer that would be most naturally represented as a density plot but I realized that I hadn’t a clue as to what the resulting image would look like. It made me very curious to find out. Luckily it only required some small modification to my m-set software to find out so I tried it, and suddenly there it was. Actually I don’t remember if I first rendered all the points or filtered out the non-escapers from the start but once I did that it was clear that it looked like a Buddha and nothing else.

Looking at that first b-brot image was one of the most surreal experiences of my life. I had to strongly question whether I might really just be dreaming. From that moment I knew that I would spend a lot of time trying to generate the best pictures I could with this technique.

MA: What gave the inspiration to view the Mandelbrot set as a 4 dimensional set?
MG: This project has gone on for over a decade now. Most of the time I don’t do any active exploration but the prints that I have hung on my walls cause me to wonder about new things to try. For instance, before coming up with the ideas for 4D renderings my images were all simple gray scale images, or at lease single color ramps. I looked at those images a lot and sort of felt bad that there didn’t seem to be a natural way to turn them into color images. Eventually I had a sudden realization that multiple images with different threshold values could be combined in the same way that astronomers combine photographs of cellestial bodies taken at different wavelengths into false color images. Suddenly I was making meaningful color images. My explorations then went inactive again for a long time. I started thinking that it was a shame that the object wasn’t really 3D instead of 2. I couldn’t think of a natural way to cast the underlying object into a 3D model but eventually if suddenly hit me that it’s really naturally 4D object! The popular Julia set is really the natural extension of the m-set into 4D but the standard rendering technique for Julia set visualizations used the same ones as typically used for the m-set. The natural application of the b-brot technique to the whole Julia set would result in a 4D density plot. I was familiar with the visualization techniques for volumetric data so it wasn’t hard to imagine using the same techniques to view 4D b-brot data projected into 2D and 3D “planes”. Hence what I called [it] the Buddhagram.

MA: Real numbers, Imaginary numbers, argh! How did you understand it so well? Some of our readers are normal non-math inclined people (myself included), Do you mind explaining a little on how you grasped the concept so well?
MG: I don’t feel that I do grasp it very well. I mean I sort of have a good feeling for the real numbers but complex arithmetic still just feels like a recipe. I don’t understand the reason that the complex arithmetic recipe is what it is. I know that it’s an indispensable tool for all sorts of practical scientific modeling but I haven’t a clue why that is so. I would love it if someone would explain that to me. Once I had those simple mathematical operations coded up I could then ignore how they worked and just concentrate on visualizing the results of using them.

MA: What do you think of math and art? Some art people say fractals aren’t art (because ‘all the work is done by the computer’, and some math people say artistic fractals aren’t math (because ‘anything can look like a fractal to the layman’). Any words to that?
MG: There is certainly art in finding beautiful fractal formulas and especially in selecting initial formula parameters and in finding interesting regions to render, color, and crop. Some computer artists go far beyond that by compositing, mashing, and otherwise altering fractal images into artistic forms but my goal is to present only the original Mandlebrot formula in as “faithful” a way as possible using the Buddhabrot technique. Beyond that there is still substantial room for artistic expression though maybe one could call it artistic presentation? I don’t think of myself as an artist though I like to think that I have an artistic eye.

You can certainly argue that fractal images are not math in themselves but fractal images are certainly indispensable when describing fractal formula, and these certainly make up an important branch of mathematics, both practically and aesthetically.

MA: Finally, what do you have to say to budding mathematical artists?
MG: The same thing that I say to anyone with a passion: Follow your passion as far as you possibly can for as long as you feel that passion. It doesn’t matter if your dream is as impractical as becoming a rock star or an astronaut because even if you don’t get to where you had originally hoped, you may end up somewhere even better (and yes, more practical). Another way to look at it is to realize that life is extremely short and that if there’s anything you want to do or feel before you die, you had better do it quick because it’s almost certain to be all over soon.