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It wasn’t until later that I learned how to render hypercomplex fractals on POV-Ray, although I must say it is a very slow way to render.
MANDELBULB 3D PRINTING SOFTWARE
How critical was this software to the development of the first 3D Fractal images? MM: You mention the “Persistence of Vision Raytracer” (POV Raytracer) multiple times on your website. The higher order Mandelbulbs certainly are an improvement, but they also have regions that look stretched out. The problem with the standard quadratic Mandelbulb is that it has some distorted regions that look like stretched out taffy. Everyone’s goal was to find a 3D formula that that could produce all the wild variety and extravagantly ornate details of the 2D Mandelbrot Set. I thought they were pretty neat, but I didn’t think they were a breakthrough. Paul Nylander: I had been working on 3D Mandelbrots for about 2 months before I rendered higher power Mandelbulbs. MM: What went through your mind when you first rendered the 8th order Mandelbulb set based on following the generalized variation of Daniel White’s original squaring formula? How long had you been working toward that discovery before it happened? I can only imagine what might have happened if Rudy had access to the same rendering capabilities back in 1990. Rudy Rucker beat everyone to the punch with his similar formula in 1990, but it didn’t attract much interest at the time because he did not have a high-quality rendering of his beast. Thomas Ludwig also played a critical role in creating the first high-quality rendering. I feel Daniel White deserves the most recognition for coming up with the best 3D Mandelbrot formula and advancing everyone’s appreciation of 3D fractals. Paul Nylander: Not very often, but I do have much respect for them. Do you still communicate with any of them? MM: You had the opportunity to engage with many of the pioneers during the early development of 3D fractals. But I continued learning new fractals and adding them to my website. I excitedly showed it to other people, but they didn’t seem very interested. I felt that I had discovered something great. I stayed up late and finally created my first complex fractal, but it was distorted and looked like cobwebs. It wasn’t until 2001 that I finally found a website that explained it in a way I could understand. So I went around my college math department asking professors for help, but many of them didn’t even know what a fractal was. I was fascinated by it and I wanted to learn how to create it, but I couldn’t understand the math. Paul Nylander: The first time I saw a picture of the Mandelbrot set fractal was at a bookstore in 1998. On my spare time, I enjoy math, science, and art. I have also worked as a C++ and C# software developer. Now I am working on surgical devices, which I must say is the best job I’ve ever had. My engineering experiences have been somewhat random ranging from plutonium detectors to Disneyland rides. My education is in mechanical engineering and physics. Paul Nylander: Hi, my name is Paul Nylander. MM: Please speak to your background, education, family life and whatever you want the public to know about you. It has been an honor and a pleasure to interview Paul Nylander who played a significant role in the discovery of the 3D Mandelbulb. Please visit his website to learn much more about the process and coding that went into the discovery of not only the first 3D Mandelbulb but the dozens of other programs he used during the process: