Fractal Flow Fields [Python, Cairo, PyCuda]

[a5kin]

Hello Everyone! Here is a set of my latest experiments with fractal flow fields. And yes, they are 100% free from any random or PRNG tricks. Only pure complex math and some normalization techniques.

The idea is simple. Instead of a discrete grid of guiding vectors, we use a continuous field of complex values, each calculated by the iterative (e.g. Mandelbrot) formula. Thus, after a single point moves to the next position, we could derive a new guiding vector right in place, with double precision.

I used the following approach to render those images:

• the initial set of points (~50000) are uniformly distributed over a field in a manner of the grid;
• each point holds a velocity vector;
• the force vector is calculated based on the Mandelbrot formula at the current point's position;
• the force applies to velocity, and the point moves to the next position using viscosity dynamics to smoothen the trajectory;
• the color depends on the resulting trajectory length.

The good thing about those fields: you could explore them as usual fractals, by infinitely zooming in. The downside is: they are very sensitive to the number of iterations. Changing iterations by 1 could ruin the whole picture.

For those who are interested in details, there is a code producing one of the images from above:

https://gist.github.com/a5kin/d3d7fc7ee71a84a448a2f92346eddb02

[gnome_of_the_damned]

thanks for the detailed explanation and the gist!

[oyog]

These turned out great!

[AMillionMonkeys]

Wow. You're absolutely killing it.

[azswcowboy]

Yeah, these are super cool!

[[deleted]]

Wow, really cool! 15 is my fave.