= The Fractal Wonderland = [[figure-float-right:/artwork/fractal-stack.gif My Fractal Animation II stack, from the “Marcio's Stacks” disk.]] March 29, 2014
by Marcio Teixeira
I have been fascinated by the Mandelbrot set for as long as I can remember—the endless coastline, the thicket of wispy branches, the army of seahorses standing to attention, the occasional child-Mandelbrot hanging on to its parent by a tendril. One of my earliest experiences with the Mandelbrot set was through a program called Super MANDELZOOM by Robert P. Munafo[1]. It was wonderous, as if receiving images from another world, yet their slow reception was anti-climatic. So I took screenshots from that program and made a flipbook-style animation to show what it would be like to free-fall into the depths of the fractal rabbit hole. { "icons" : [ ["Marcio's Boot Disk", "boot-hd", "/disks/mac-marcio's-boot-1.0.qed"], ["Marcio's HyperCard Stacks", "floppy", "/disks/mac-marcio's-stacks-1.0.image"] ], "class" : "float-center" }
So what exactly is the Mandelbrot set? It's just an equation. An equation that when written out in computer code is actually quite simple; that same computer code then takes us to a world that is far too complex for the thing that created it.
I don't recall when I learned enough about math to write my own Mandelbrot program—even after I was formally introduced to imaginary numbers in school, I still saw them as having no application beyond creating the Mandelbrot universe. As something that had captured my imagination for so long, it was an accomplishment to write my own Mandelbrot program, even if I did not exactly understand how it worked. [[figure-screenshot:/artwork/fractal-explorer.gif My own Fractal Explorer program, from the “Marcio's Apps” disk.]]
I can't shake the feeling that the equation that purportedly gives us the Mandelbrot set is a red-herring; it can create the landscape beyond it no more than a door can create what we experience after we step beyond its threshold.
And so, I wonder, where lies this beyond? If not in the equation itself, then where do the frothy whorls and eddies of the Mandelbrot landscape exist? I do not know the answer to that question—I probably never will. But the Mandelbrot set became a cliché for me; it became a visual "Hello World!", a small program I could write in any programming language, for any computer I encountered since, whenever I had a moment to step beyond that threshold and into another realm. == Explore == { "icons" : [ ["Marcio's Boot Disk", "boot-hd", "/disks/mac-marcio's-boot-1.0.qed"], ["Marcio's Apps", "floppy", "/disks/mac-marcio's-apps-1.0.image", {"drive" : "fd2"}] ], "class" : "float-center" } == References == # http://mrob.com/pub/muency/supermandelzoom.html