# Lori-Anne Gardi

Dear Mandelbrot Set,

I have always been a great fan of mathematical art. I have been
generating computer art since the Vic-20 / Commodore-64 days. I played
with many different equations; generating one interesting image after
another. But, when I first met you, that infamous day in 1985, I knew
I could never look at another mathematical equation. You were the ONE
for me. Never could I have imagined such vast complexity emerging from
such a simple formula, z=z^2+c. You are a great artist. Your stunning
patterns outshine all the stars in the galaxy. You are a great
mathematician. Complexity from simplicity? Brilliant! And you are a
great teacher. Everything I know about fractals and the universe, I
learned from you.

Eternally yours...

Buddhabrot and Bubblebrot are of the lesser known renderings related to the Mandelbrot set. Although they were both generated using the same mathematical formula, z = z^2 + c, these two images are qualitatively very different. Buddhabrot (right) was created using only the escaping points from the complex plane and Bubblebrot (left) uses only the non-escaping points. I was one of the original experimenters of this non-standard rendering technique (invented by Melinda Green). I coined the term Buddhabrot and developed an algorithm to detect the non-escaping points, significantly improving the rendering time. Buddhabrot and Bubblebrot were generated simultaneously. It took ~1.5 hours and 1.7 billion iterations to compute on a standard PC.

The Mandelbrot set literally lives in the complex plane. This is why it is special. It is found that each point from the complex plane, when iterated through the function z = z^2 + c, generates a different trajectory or picture. The figure in this image is one of an infinite number of possible trajectories. (Others are featured in a paper I wrote called "The Mandelbrot Set as a Quasi-Black Hole".) The algorithm used to generate SINGULARITY is the same algorithm used to generate BUBBLEBROT and BUDDHABROT only here, we are studying the trajectory of ONE complex point only. The art piece features the equation used to generate the image along with the real and imaginary components of the initial complex point. The iteration count is also shown.