These pictures are breathtaking. They remind me of gothic cathedrals, but more stimulating, deeper, and even more beautiful. Knowing they are mathematically generated gives me a feeling not unlike ecstasy.
This 3D creation is impressive, but the original Mandelbrot set has far deeper impact on me [not parent poster]. Since I was a kid I've been fascinated by these forms; by the infinite intricacy, the simultaneous multilevel self-similarity -- it just sucks you in. It's beautiful but also at times I can feel it to be sickening and horrifying, like a poison. I can't help feeling there is some kind of essential life force in such constructions, in the spaces between order and randomness. It also reminds me of the ideas I've read behind William Blake's "The Marriage of Heaven and Hell".
The first time I discovered the Mandelbrot set was an incredibly emotive and beautiful experience. I immediately moved to Wikipedia to further research it, where I found out about the Julia fractal sets that can be formed from the same equation by seeding it with a specific complex number.
Then I found this image mapping Julia sets on the complex plane by their seed values.
It's been a very long time ago since I first saw a mandelbrot but it must've been something like "cool / whatever" and only after learning more about it I started to appreciate it.
Seeing the Mandelbulb pages a couple of months ago through HN I was really in awe and also found it very inspiring since it pertains to some of my pet projects.
Is it possible for you to explain why it induces you with dread? I really can't understand that.
I never thought I'd feel compelled to write a poem on HN:
There is this incredibly slow machine,
analyzing everything relevant in these passing things...
arms moving and seeing.
Seeing and slightly clutching some very few things with beings.
Every instant, a thing goes dimmer,
until slowly few remain.
These are the harvest of this incredibly slow machine.
I see the Mandelbrot as a surface on a much larger surface, and that surface on an even larger surface (and so on). It is an infinity that I cannot begin to comprehend, and at the end of it all... the best phrase I can think of to describe "the whole" is: an incredible slow machine.
The Madelbrot is a virtualization and a sterilization -- it's a glimpse of something much grander, and that grander thing, that I called the incredible slow machine, permeates into reality and appears to determine the outcome of everything. Its arms stretch and grasp every little detail of every universe and we can see the evidence of its existence in the ferns as well as the galaxies.
A hugeness that seems indifferent to our presence.
Is it possible that our universe is much like the Mandelbrot set? That an infinite number of slight variations and radical variations of universes exist?
From the very bottom, the numbers are calculated and fed back into the equation. The result is that we're an extension of a fractal finger. On an arm of the machine. An arm on an arm on an arm on an arm....
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Addendum: I'm still not satisfied with my answer for you, but I'm sure you can at least sense the unease some might feel. I can actually go on all day about this, and I would have to if I wanted to make any sense. So I have to stop myself because such energy needs to go into my writing.
These days I'm pretty immune to existential dread. There was a long stretch of my life where I could not stop poking at this stuff. And, frankly, I think I've emerged slightly insane. It's part of the reason I stopped studying math; it got too much for me, and I've shifted my focus onto writing.
Heh, but if you're a fan of GEB you know that you cant completely escape. That the strangeness still exists in writing.
Thanks for the expansive answer. I think I understand the feeling of dread you were talking about now. I get it when trying to comprehend the universe even though I'm aware of the scientific theories about it I can't help but let my mind wander about how big it is or what it really means for it to be infinite and if it weren't infinite what would it be in and what would be beyond it, etc. etc. Those little meanderings haven't really changed since I was 8 or so and I'm now 35 and I can just touch what it would be like to be insane when going long and deep enough.
A healthy dose of psilocybin mushrooms is what Bill Hicks recommended. (and so do I!)
Also, while I have read GEB since it's sort of required reading, I'm not really a fan of it. This is probably heresy here on HN but like all other of Hofstadter's books I can't stand his huff-puffery about himself and really it distracts from the interesting content in his books. I'm sure he's a nice guy and brilliant mind and it's most certainly a character flaw of mine but his writing style just doesn't click with me. I've tried multiple times to put it past me but have been unsuccessful so far.
