4 ms·

What determines alpha on those images? On any attractors really? You end up with an infinitely large set of points between say -1.5 and 2.0. How does that end u

What determines alpha on those images? On any attractors really? You end up with an infinitely large set of points between say -1.5 and 2.0. How does that end up being graphed. Perhaps that is magic/beauty of it.

taneq 11y ago
I've done similar images in the past and the approach I used was: 1) Choose a target image resolution, and set up a square array of that size, initialized to zeroes. 2) Decide on the bounds you want to use, and linearly map coordinates into the target image. Say you want to graph x in the range [Xmin, Xmax) and your resolution is Xres, then pixel_x = (int)((x - Xmin) * Xres / (Xmax - Xmin)) (Note that if you have a higher-dimensional attractor you'll need some form of projection down to two dimensions.) 3) Iterate your attractor equation (starting point doesn't matter because it's an attractor). Each iteration, increment the pixel that matches your current coordinates. Stop iterating when you land on a pixel with a value above some preset. 4) Apply a palette to your pixel values to turn it into a nice picture like the ones linked here.
gunn 11y ago
I think it's determined by resolution and number of iterations. I wrote a quick JS vesrion using the provided formulas: http://bl.ocks.org/gunn/87401cb547cc2ee5b5ec http://bl.ocks.org/gunn/87401cb547cc2ee5b5ec
- tonetheman 11y ago
  Your code and mine look really similar. You did a lot more points than I did. I will try that out and see if makes mine less "pointy." ha
notthegov 11y ago
Could you elaborate or suggest any references? It sounds like you are saying something that appears chaotic forms some coherent beautiful image? I know alpha refers to many things but one of those is the fine-structure constant. There's some remarkable beauty in it because it unites electromagnetism, relativity and quantum mechanics. And this is why many thought the reciprocal of alpha (137) would become as important as 0 and Pi. I am assuming though none of that relates to fractals and that alpha in this context refers to the angles?
- Twisol 11y ago
  "Alpha" in this context probably refers to opacity, the A in RGBA. GP is making a comment on the apparent translucency of the filaments that comprise the attractor.
- tonetheman 11y ago
  Yeah my question really is how do you color these things in the render. I quickly wrote something that would output the numbers and mapped those to points on the screen. But it just ended up looking like that. Points on a screen. The images on the site looked like they had alpha... or used a much better idea than mine of just using points on a plane.

taneq 11y ago

I've done similar images in the past and the approach I used was: 1) Choose a target image resolution, and set up a square array of that size, initialized to zeroes. 2) Decide on the bounds you want to use, and linearly map coordinates into the target image. Say you want to graph x in the range [Xmin, Xmax) and your resolution is Xres, then pixel_x = (int)((x - Xmin) * Xres / (Xmax - Xmin)) (Note that if you have a higher-dimensional attractor you'll need some form of projection down to two dimensions.) 3) Iterate your attractor equation (starting point doesn't matter because it's an attractor). Each iteration, increment the pixel that matches your current coordinates. Stop iterating when you land on a pixel with a value above some preset. 4) Apply a palette to your pixel values to turn it into a nice picture like the ones linked here.

gunn 11y ago

I think it's determined by resolution and number of iterations. I wrote a quick JS vesrion using the provided formulas: http://bl.ocks.org/gunn/87401cb547cc2ee5b5ec http://bl.ocks.org/gunn/87401cb547cc2ee5b5ec

tonetheman 11y ago
Your code and mine look really similar. You did a lot more points than I did. I will try that out and see if makes mine less "pointy." ha

notthegov 11y ago

Could you elaborate or suggest any references? It sounds like you are saying something that appears chaotic forms some coherent beautiful image? I know alpha refers to many things but one of those is the fine-structure constant. There's some remarkable beauty in it because it unites electromagnetism, relativity and quantum mechanics. And this is why many thought the reciprocal of alpha (137) would become as important as 0 and Pi. I am assuming though none of that relates to fractals and that alpha in this context refers to the angles?

Twisol 11y ago
"Alpha" in this context probably refers to opacity, the A in RGBA. GP is making a comment on the apparent translucency of the filaments that comprise the attractor.
tonetheman 11y ago
Yeah my question really is how do you color these things in the render. I quickly wrote something that would output the numbers and mapped those to points on the screen. But it just ended up looking like that. Points on a screen. The images on the site looked like they had alpha... or used a much better idea than mine of just using points on a plane.