4 ms·

I'd bet a thousand dollars that when graphed, these islands of regularity will correspond to the graph of the Mandelbrot set.

eszed 2y ago
Why Mandelbrot, specifically?
- big-green-man 2y ago
  I am going out on a limb and speculating that these stable sets of conditions correspond to Julia sets by some mathematical relationship and that the underlying fundamental principle is the same. https://en.m.wikipedia.org/wiki/Julia_set https://en.m.wikipedia.org/wiki/Julia_set
  - m3047 2y ago
    The Mandelbrot and Julia sets are the outcomes of specified functions and have a relationship with each other. But yeah I would speculate that something similar, in the way that a Mandelbrot set is self-similar, would be observed in at least some circumstances. Gave you a vote for that. Edit: reading the article I can see that Julia sets are defined separately from the Mandelbrot set and the corresponding Julia set(s) are an example. So maybe you're right. I'm not really a mathematician, I just use math to get stuff done.
moi2388 2y ago
I’m willing to take that bet.
- big-green-man 2y ago
  So what do you think the math is going to look like about the starting values of these stable states? I'm speculating that they correspond to Julia sets by some fundamental relationship.
  - rcxdude 2y ago
    1) They're not stable, they're regular. The point is these areas of the state space have similar outcomes if they are perturbed slightly, as opposed to the result being random 2) there's literally a plot of it in the article, and while it shares some properties with the mandelbrot set (symmetry about the X axis, is a fractal), it doesn't resemble it at all.
SideburnsOfDoom 2y ago
Will it be that fractal? it seems tenuous. Will it be a fractal? That would make sense.
pixelpoet 2y ago
I've spent a good portion of my life working on fractal software, trying basically every fractal rendering algorithm there is, reading everything I can about it, managing fractal art communities and organising meetups... so I'm obviously very pro-fractals biased, and even so, I'm curious what makes you conjecture so strongly that 3-body stability islands would have anything to do with the Mandelbrot set. Why that one in particular, over the vast infinitude of possible fractal shapes?

eszed 2y ago

Why Mandelbrot, specifically?

big-green-man 2y ago
I am going out on a limb and speculating that these stable sets of conditions correspond to Julia sets by some mathematical relationship and that the underlying fundamental principle is the same. https://en.m.wikipedia.org/wiki/Julia_set https://en.m.wikipedia.org/wiki/Julia_set
- m3047 2y ago
  The Mandelbrot and Julia sets are the outcomes of specified functions and have a relationship with each other. But yeah I would speculate that something similar, in the way that a Mandelbrot set is self-similar, would be observed in at least some circumstances. Gave you a vote for that. Edit: reading the article I can see that Julia sets are defined separately from the Mandelbrot set and the corresponding Julia set(s) are an example. So maybe you're right. I'm not really a mathematician, I just use math to get stuff done.

moi2388 2y ago

I’m willing to take that bet.

big-green-man 2y ago
So what do you think the math is going to look like about the starting values of these stable states? I'm speculating that they correspond to Julia sets by some fundamental relationship.
- rcxdude 2y ago
  1) They're not stable, they're regular. The point is these areas of the state space have similar outcomes if they are perturbed slightly, as opposed to the result being random 2) there's literally a plot of it in the article, and while it shares some properties with the mandelbrot set (symmetry about the X axis, is a fractal), it doesn't resemble it at all.

SideburnsOfDoom 2y ago

Will it be that fractal? it seems tenuous. Will it be a fractal? That would make sense.

pixelpoet 2y ago

I've spent a good portion of my life working on fractal software, trying basically every fractal rendering algorithm there is, reading everything I can about it, managing fractal art communities and organising meetups... so I'm obviously very pro-fractals biased, and even so, I'm curious what makes you conjecture so strongly that 3-body stability islands would have anything to do with the Mandelbrot set. Why that one in particular, over the vast infinitude of possible fractal shapes?