Fractal Software > Programming

 Orbit trap with Superformula

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This document piqued my curiosity and I finally decided to try to implement an orbit trap algorithm with superformula:

The algorithm that I have developed for FFExplorer performs a complex plane analysis using the equation described in the image, as follows:

* Initializes the values of m, n1, n2, n3, a y b with the values entered by the user.
* It traverses the plane and, for each point to be analysed p, gives φ the value of its phase, with which it solves the equation and obtains a radius r.
* Find the modulus of the complex number represented by the values of r and φ in its polar form.
* Check if the modulus of p is less than or equal to the modulus calculated in the previous step, in that case the algorithm considers that the analysed point is inside the shape and proceeds to colour it, otherwise it is not coloured.
In this way, an infinite number of shapes can be achieved that provide excellent results in fractals.


Here you can see the result of using a supershape in the colouring of a fractal.

Will you share the source code? I would like to compare notes re: and

I think the super shape has potential in fractals for more than orbit traps.

I am not going to copy paste my original code because I use MVC (model-view-controller): These are small distributed code capsules (models), whose interactions with each other are orchestrated by controllers (too much code and cross references for a really simple algorithm).

However, my instructions are precise so that whoever wants to do it can take it into their own programming language without difficulty, and if I put a pseudocode it would repeat exactly the instructions that I have given you, but with instructions from an invented language, which does not seem useful to me.

--- Quote ---I think the super shape has potential in fractals for more than orbit traps.
--- End quote ---
Yes, in your link I see that you have used the formula differently. The possibilities are many :)

You can see in the image the difference between using colouration by escape versus the colouration by distance to supershape.
The formula of the fractal is a classical Mandelbrot.


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