that's a really nice page you've got there; the stuff about music is of particular interest to me as i've been putting together knowledge to try and make some procedural sound/music at some stage
Would that be the "Is there such a thing as perfect taste in music?" page? Yeah, the whole area of computer generated music has fascinated me for a while too. Let me hear if you generate anything interesting!
Obviously, people have attempted fractal music, but the results from what I've heard don't seem all that good really. Fractal sound effects though; that could easily produce some very interesting results.
I've also thought about some of those maths puzzles, and a few of them might be interesting to tackle at some stage... do you have solutions for all of them?
Ah, the impossible math page. The only solutions I have figured out are for the early puzzles
In particular, the 'Snooker Table of Doom' may rely on a fast analytical technique, otherwise, simulation of that is going to be quite tricky indeed I imagine
lemme know when you've got something that needs rendering, ray tracing is my speciality
Sure thing! You may want to try something from below if it's easy enough, though I'm not sure how interesting they really are (I'll make an detailed animation soon probably).
cool, which caley tables are you working with at the moment? any images?
At first I was experimenting with the expanding the basic complex multiplication calc to 3D using various techniques, but now I'm trying a more visual approach. Basically, complex multiplication can be seen as 'rotating' the point around the origin (adding both angles together). Therefore I'm trying to rotate on the X (or Z) and Y axis in 3 dimensions. There are a number of ways of doing this, but for all I know, I could be barking up the wrong tree - it's difficult to say for sure when doing this kind of stuff!
Images? Yeah sure. Two of my most 'successful' results include these. They show cross sections, or slices through an apple, but I might make an animation to show the detail better.
The problem with this first one is that although the Mandelbrot shape is apparent, the Z axis is more or less 'extruding' the data rather than exhibiting its own detail:
This second one is an improvement, but the Mandelbrot shape is not as clearly defined. The 'bulbs' also seem to 'evolve' throughout the Z axis (grow and then shrink into nothing which is what we're looking for) to a degree, but final judgment of its potential will come once I've made the anim.
as for the "3d mandelbrot set", well, the mandelbrot set is intrinsically 2d, so a 3d fractal it'd have to be something else wouldn't it?
Well in the same way that the Sierpinski carpet is a 2D version of the 3D Sierpinski sponge, I'm hoping one may generalize the mandelbrot to 3D or to any arbitrary dimension for that matter. It would still (hopefully) retain the basic Mandelbrot shape characteristics.
i've made 370 without doing so, it's definitely not required