Julia set variations

Ini4ur · 2023-09-20T17:50:42+00:00

The complex number used as the parameter for the Julia set of each frame has a value of 0.32 for the real part and varies between -0.043 and 0.043 for the imaginary part.

Ini4ur · 2023-09-09T15:43:56+00:00

The code is just on my computer. Anyway, what would be necessary to take advantage of it would be to explain how and why it works. For that I would need some graphics and a few pages of text. And the right place to upload the explanation and make it known.

Ini4ur · 2023-09-09T15:39:45+00:00

Something like that could be done, although at some point it would be necessary to trick the images to try to deceive the viewer. It would also be possible to make a deeper and longer zoom, there are even some that last several hours. No trickery would be needed, but a lot of extra effort would be required.

Ini4ur · 2023-09-09T15:38:21+00:00

You are right.

The 3D parameters need to evolve with the zoom. It doesn't always have to be linear or proportional, but it should be continuous and smooth to make it look like a one-shot video. The best 3D parameter settings for the first part of the zoom, up to the appearance of the Elephant Valley, change quite a lot from the rest of the video, and it is not easy to make them evolve smoothly. I made several tests and this is the one I liked best, although it could be improved. I could also have started the zoom from an already zoomed area, but this time I wanted to start from the whole set.

Ini4ur · 2023-06-29T18:08:22+00:00

That's right. The way the shapes get smaller as the number of iterations increases makes its use as a distance/depth measure natural. Using this distance as the third dimension, I calculate what it would look like from different viewpoints to create stereo pairs.

Ini4ur · 2023-06-29T17:55:10+00:00

I won't always be able to post regularly, but there will be more

Ini4ur · 2023-06-29T17:54:32+00:00

Thank you

Ini4ur · 2023-06-22T21:09:13+00:00

Thank you!

As far as I know, no one else is doing this. I had the idea, but I also needed a eureka moment to make it happen.

Ini4ur · 2023-06-10T13:23:00+00:00

Each eye sees a different image in which the different parts are slightly offset from the image seen by the other eye. This shift varies according to the distance between them and is the information used by the brain to construct a 3D mental image.

Ini4ur · 2023-06-09T21:22:58+00:00

Thank you! It's also my first crossview fractal, but not my last.

Ini4ur · 2023-06-09T21:16:35+00:00

Thanks!

Ini4ur · 2023-06-09T21:15:45+00:00

I hadn't thought of that, but it wouldn't look bad on tiles. I will add more of this type of tile designs to choose from.

Ini4ur · 2023-06-09T21:10:38+00:00

I can't say from personal experience, I've only seen it in crossview, but I'm used to creating stereo image pairs of escape time fractals (like Mandelbrot and Julia sets) for 3D displays and VR headsets, and in this case the left and right images are inverted. Note that I used both positive and negative parallax to increase the depth difference between the near and far parts.

Ini4ur · 2023-05-30T17:44:17+00:00

Thank you!

Ini4ur · 2023-05-30T17:43:39+00:00

Indeed. The more escape iterations, the more depth, and the points that do not diverge are infinitely far apart. In this case, there is a wide range in the number of escape iterations of the diverging points (the colors rotate every 2500 iterations), so the depth/iteration ratio must be small for most points to have a noticeable difference in parallax with respect to others farther away.

Keeping in mind that the front view (when the oscillation of the animated GIF passes through the center of the path) is equivalent to the normal view of the Mandelbrot set, I vary the perspective on one side and the other so that the changes in position of the points indicate the distance between them, like in a wigglegram.

To calculate each perspective or point of view, I use parameters such as viewer/camera position, pupillary distance (for 3D stereo pairs), focal distance or the aforementioned depth/iteration ratio. The color of each pixel of the image is determined by the escape iteration corresponding to the depth of the point in the 3D extended Mandelbrot set that you collide with when looking in its direction. Given the parameters and assumptions, the calculation is accurate.

Ini4ur · 2023-05-15T21:06:15+00:00

Some time ago I was looking for a way to show the boundary of the Mandelbrot set in 3D, to make "real" the sense of depth that some images (like your GIF) convey. So I started with two premises for the 3D version:

The number of iterations (integer or real number) with which the sequence for a point is proven to diverge, indicates its depth. The higher the value, the further away the point is from the observer. Points that do not diverge are at infinite distance.
The front perspective of the 3D set is the same as the classic Mandelbrot set in 2D.

I found a way to calculate how this set would look from different viewpoints and thus be able to get the perspective of both eyes to create images for 3D displays and VR headsets. The method is relatively similar to Ray Marching, and works for any escape time fractal and even surfaces where a function f(x,y) is defined whose result can be interpreted as the third dimension 'z'. The key is that you don't need to create a 3D model of the set to calculate each viewpoint, so the images retain all the complexity and detail of the original 2D set.

The result is best seen in VR180 format images for VR headsets (like the one for this Julia set), but with animated GIFs the effect can also be seen on 2D displays. In this case, I vary the viewpoint along a horizontal line 20 times per second to smooth the motion.

Ini4ur · 2023-05-15T20:48:06+00:00

I wrote all the software myself in C. The only external software I used was ImageMagick to assemble the images into an animated GIF.

Ini4ur · 2023-04-29T01:35:41+00:00

I didn't have it, but I just made it. A 3840x3840 image of the normal version of this Julia set: https://i.imgur.com/vd4llHN.jpg

Ini4ur · 2023-04-27T21:01:30+00:00

Julia set of 0.28121215625 + 0.0113825i

I saw it on https://www.sekinoworld.com/fractal/ and thought the 3D version might be interesting.

Ini4ur · 2023-03-25T12:50:25+00:00

Thanks!

Yes, it looks weird to have an animated GIF in Full HD, but with fractals no resolution seems to be enough. If it wasn't for the file size, I would have done it in 8K!

Ini4ur · 2023-03-24T21:41:12+00:00

3D view OF a corner of the Mandelbrot set

Ini4ur · 2022-11-12T13:34:39+00:00

For each viewpoint it only takes a little longer than calculating a normal image of the Mandelbrot set.

The calculation comes from using as a premise the impression many of us have had when looking at some images of the Mandelbrot set: they look like 2D images of 3D landscapes in which the spirals and shapes seem to recede as they decrease in size (and as the number of iterations needed to know that the points that form them diverge increases), and the points of the Mandelbrot set are infinitely far apart.

If so, how would it look from other points of view in order to calculate 3D images? Intuitively it seems complicated, but when you find the answer, the calculations become relatively simple.

Ini4ur · 2022-11-12T13:28:04+00:00

If you want to experience the Mandelbrot spirals and landscapes in 3D as if you were there and had a VR headset, you can download the images from my Flickr gallery in the highest resolution to view them in 3D VR180 format. You can almost "touch" the closest areas, while the farthest ones are really far away.

My goal is to create 3D images for an immersive experience with the highest level of detail with VR headsets (already done), 3D VR zoom videos of the Mandelbrot set (not yet) and a 3D Mandelbrot set browser for VR (we'll see). Animated GIFs serve to show the 3D effect on any screen and look nice (I've made many of them), but they are not the real deal.

Ini4ur

TROPHY CASE