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Author Topic:  Fractals Made of Fractals  (Read 571 times)

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Offline AranLeer

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Fractals Made of Fractals
« on: April 09, 2020, 06:55:58 PM »
Hello Everyone.
I'm sure I'm not the first one to do this, but I still think it's worth sharing, since it's an interesting concept, and gives some really silly and mind-bending results.

As you no-doubt gathered from the title, the idea is that it is possible to create a fractal whose contents made from another fractal entirely.
But really, this is a more general concept of applying any shape to a fractal's space-warping formula.

Most people here know how a fractal is created through an iterative formula, but may not stop to think about what the formula is actually doing in a more physical sense.

Here's one way to think of it in a physical way:
Essentially, most fractal formulas can be thought of as a sort of space-warp or space-fold, moving the points in space from one point to another. Then, after applying that space warp, we go ahead and apply it again.
We then apply this to the space as many times as we want (which is what the iterations are).
And then after we're all done doing all the space-warps, we color in a circle on top of the warped space.
Then we un-warp space, and the resulting shape is our fractal.

So essentially, a fractal is just a circle drawn on top of warped space.

(A pretty cool way to think of it, I would say ;) )

But - there is no reason that we have to use a circle as the base shape of the fractal.
We can use literally anything, although most simple shapes only make small differences in the final outcome.

One of the things we can use instead of a circle that is quite fun is a repeating image, which is a cool way to see exactly how space is being warped.
I'll add some examples down below, so you can see what it looks like.

But while playing around with adding images as the base shape of the fractal, I ended up adding previously-rendered fractal images as the base shape of the current fractal.

This gave me the idea that it would actually be possible to calculate one fractal, then using the final coordinates of the calculations, go ahead and calculate a completely different fractal.
So - essentially - warping space using one fractal formula, then taking that warped space and warp it again using a different formula.

So, fractals being made of other fractals.

And this process can be expanded beyond 2D space.
3D fractals can also use other base shapes than a sphere, such as any 3D shape, 3D model, or even other 3D fractals.

Anywho - that was probably way too long of a post for such a simple concept - but it's one that I find quite fun.

Linkback: https://fractalforums.org/index.php?topic=3412.0

Offline AranLeer

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Re: Fractals Made of Fractals
« Reply #1 on: April 09, 2020, 06:58:57 PM »
Fractals Made of Images

Offline AranLeer

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Re: Fractals Made of Fractals
« Reply #2 on: April 09, 2020, 07:01:13 PM »
Fractals Made of Other Fractals

Offline hobold

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Re: Fractals Made of Fractals
« Reply #3 on: April 09, 2020, 07:24:34 PM »
The devious application of this idea is to mix the irreconcilable: power 2 minibrots arranged in threefold symmetry by the Z^3 mandelbrot and the like. Stumps the experts, and leaves the laymen wondering why the experts are stumped. :)

Offline gerson

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Re: Fractals Made of Fractals
« Reply #4 on: April 10, 2020, 02:16:36 AM »
Take a look on images done with an unreleased version of raimuraito:
http://www.wack.ch/fame/hot/kodhot.html
Choose Yasuo Kamei's gallery to see how it insert a fractal inside the orbit trap.

Mutatorkammer
https://fractalforums.org/index.php?action=downloads;sa=view;down=1
also use images inside fractals:
https://fractalforums.org/index.php?action=gallery;su=user;cat=4;u=2

Offline Caleidoscope

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Re: Fractals Made of Fractals
« Reply #5 on: April 10, 2020, 12:26:43 PM »
I also love to use fractals to create fractals, or/and use images to get a certain effect.
For example:

Using mandlebulb/box fractals to get another, in my opinion nice result:

« Last Edit: April 10, 2020, 12:45:46 PM by Caleidoscope »

Offline Caleidoscope

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Re: Fractals Made of Fractals
« Reply #6 on: April 10, 2020, 12:44:34 PM »
Or these, made with fractals:

Offline quadralienne

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Re: Fractals Made of Fractals
« Reply #7 on: May 02, 2020, 11:36:18 PM »
I started with the image strategy many years ago, but soon moved on to actually calculating the inner fractal recursively ... here are some new results: https://www.youtube.com/watch?v=tLxMgtoWjvg

Offline gerson

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Re: Fractals Made of Fractals
« Reply #8 on: May 03, 2020, 03:03:08 AM »
Fractal Zoomer can insert images and fractal's images inside an orbit trap.
See the image I posted on Reply #10 at:
https://fractalforums.org/fractal-image-of-the-month/70/-fractal-image-of-the-month-contest-november-19-and-the-winners-are/3170


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