Quaternion Julia Set Shape Optimization

We present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi-resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non-linear transformations.

[Tadesan]

First thought is that this is brilliant.

Second thought, I'm surprised that it seems so effective. I was suspecting that you were going to say something like; "we have demonstrated that it is possible but to actually do it would require ten to the ten to the ten to the five hundred iterations...
Bravo!

[hybridmicewithsupersemenin]

oh, i have been searching all over for themes that involve this.. So i don't really understand why i first saw it now!? anyway.. Source code and everything.. Thanks! keep up the non-linear transformations!

[camilogallardo]

i was just wondering whether julia sets could be made in any desirable shape and how they would look when generated by quaternions when i came upon this.
it is outstanding work, congratulations.

btw, it would be just amazing if this mathematical framework could be applied to accurate collision checking in simulations & videogames. do you think such approach to be a reliable possibility for the optimization of computation time?

[Alpacnologia]

So the algorithm you found renders Julia sets in 3D, then compares them with a desired shape until it finds a fitting one?

[alanhere]

How many decimal places is the (x, y, z, w) seed (position) for one of these examples?