Representing Fractals as an equation

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Offline tk1221

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« on: March 28, 2019, 08:38:39 PM »
Hi everyone!
This is my very first post in this forum(so it might be a really basic question, sorry if this was obvious to anyone  ;D), and I wanted to ask if it is possible to represent a single fractal art with a single equation.
I'm aware that there are different formulas for different fractal types(shapes), but I realized that those are just general equations and not equations with specific values and functions.

I'm really interested in creating fractal arts that can each be represented by a single equation, which was the main reason that made me fall in love with fractals.
If it's possible to represent each art with a single equation, can anybody recommend me a software that is capable of such features?
I am bombarded with so many softwares like ultrafractals and mandelbulb3d, but I'm not sure which program to start with.

I would really appreciate if anyone can help me start with this mysterious journey!!

Offline claude

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« Reply #1 on: March 28, 2019, 09:16:48 PM »
You need to give values to the general variables in a fractal formula to generate an image.

Thus each actual image is from a specific formula, which is a constructive recipe for creating the image.

The specific formula may be quite large, including eg the 1024 colours in the palette sequence in Kalles Fraktaler 2, or the source code for all the included .frags in Fragmentarium, etc.

For example, the general formula for the Mandelbrot set is z→z≤+c but until you determine which range of c values to plot, and which colour scheme to apply, it's still abstract maths.

To get started with writing fractal equations I would recommend Fragmentarium (requires a bit of programming for full impact, but you can pick that up as you go along starting with the examples), as you can modify formulas and see the results almost instantly.

Offline tk1221

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« Reply #2 on: March 29, 2019, 01:45:14 AM »
Thank you so much!
I will try Fragmentarium and look for some tutorials to start playing around with it.
I'm fairly experienced with programming, so hopefully that wouldn't be an issue.


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