Back in the 1970s and 1980s, mathematicians working in an area called dynamical systems made use of the ever-advancing computing power to draw computer images of the objects they were working on. What they saw blew their minds: fractal-like structures whose beauty and complexity is only rivalled by Nature itself. At the heart of them lay the Mandelbrot set, which today has achieved fame even outside the field of dynamics.
The Mandelbrot set is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers.
The Mandelbrot set is an incredible object that equals infinity. It’s really amazing that the simple iterated equation Z = Z^2 + C can produce such beautiful works of mathematical art.
“There’s a pattern to the chaos” of the Mandelbrot set, a fractal construction that contains infinite complexity. Artist Bill Tavis has been fascinated with fractals since his youth, when he was an excellent math student. Though he pursued a career as an artist, not as a mathematician, he’s come full circle with the Mandelmap, an intricate map that celebrates the fascinating geometry of fractals.
“Arising from a very simple and compact formula, the Mandelbrot set” — named for mathematician Benoit Mandelbrot — “is stunning when seen as a whole … but its true wonders appear when you try to look closer at the border,” Travis says. It’s impossible to include the entirety of the infinite set in any visual representation, but Tavis hopes the poster will inspire artists, mathematicians, and everyone else to “think about fractals and our world in a new way.” See more of the Mandelmap’s intricate details here.
Going far down the abyss of theoretical thoughts I introduce:
(Take a deep breath, the title is as long as the immense depth of the abyss of thoughts I am in right now.)
“Microcosm, Mesocosm and Macrocosm in the Eye of the Fractal - War between Quantum Mechanics (Microcosm) and General Relativity (Macrocosm) excerted in the Human Mind (Mesocosm) finding Peace in Phase Transitions”
As I made this photomanipulation many abstract thoughts clashed together.One part is an illustration of the universe (macrocosm), another part is neurons (mesocosm) and the other part is the fractal pattern (microcosm).In addition I have to say that all three parts of this impossible triangle are examples of fractals, may it be neuronal networks, the universe itself or the mandelbrot set - it’s all fractals.
oh, it’s just a pun with amanda’s name. i’m pretty sure that the left-most pic of the tweet is from the one scene where amanda’s having an attack in the parking lot. the pattern is called a mandelbrot set, which is basically a set of number that splits into infinite fractals when it’s plotted. they’re pretty sweet, actually. i don’t think it’s strictly relevant to the plot but it’s kinda funny that the title of the set is almost in her name
Dave McGuire had one of my favorite exhibits at VCF East X. He brought along his PDP-8/E, PDP-11/34, another PDP-11 (I forget which model), a VAX-8250, a handful of DEC terminals, and a few other things – Dave brought alot of stuff.
I’m pretty sure he was the largest power consumer at the event. All kinds of fun stuff was set up for folks to play with at their leisure. There were disk packs galore, a few floppy drives, some display-only paper tape readers, and a nice variety of terminals.
I spent a great deal of time playing with the PDP-8/E hooked into the VT-52 which was labeled as a “decscope” – it was massive! I fired up BASIC and programmed a few little things to entertain myself (namely that pyramid looking graphic). The Mandelbrot set was not my code. I also keyed in a sine wave program that was on hand to see how it looked on screen.
I also accidentally crashed the PDP-8/E by addressing a printer that wasn’t there while trying to list the contents of the directory I was in. OS/8 on a PDP-8 is very foreign to me, and as intimidating as it was to have access to this system without really much knowledge of how to handle it, damn it was fun! I wish I knew FORTRAN, or I would have played with that too.
Numbers are messed up. Math is messed up. How does something as dumb as ordering things lead to something as ridiculous as the four dimensional infinite fuckery of the Mandelbrot set. What the fuck. The calculations made to create this thing aren’t even that complicated. This is nonsense. This is like fishing for minnows and finding Cthulhu. What is *in* numbers that leads them to contain this stuff? Is it even possible that there are other universes that don’t have Mandelbrot sets like this? I can think of an alternate universe where light is faster, but I sure can’t think of one where math doesn’t work the same.