Tips on speeding up Scratch-based fractal programs?

[greentexas]

I am working on a program that plots fractals on Scratch. It is called Dinkydau (a reference to the YouTube user of the same name) and has many features. It is awfully slow unless you are using http://phosphorus.github.io/ to run it. Even then, it is much slower than programs like Fractal Extreme and Ultra Fractal.

Any tips on speeding up a fractal program for you Scratch users out there?

[Fracticality]

I can tell you what I know from my own experience. Firstly, I work in Python, which is probably not recommended by anyone for a fractal program. So maybe you won't find my advice very relevant.

I started my fractal program by iterating the pixels one by one. I can't imagine a slower method. I had to print the progress as it was working just so I could know it was working. I sped it up first by using multithreading, so multiple processor cores could handle the load. An easy way is to divide the image into quadrants or something similar. A better way is to divide the pixels directly. With N threads, every thread (from 1 to N) computed only the pixels where the pixel number % N == thread number (aka, divide pixel number by number of threads and compute where the remainder equals the thread number). This divides the pixels as evenly as possible. This gave me speedups of up to 4x faster than the original method.

I abandoned the project for a few months after this. In that time, I learned from tinkering with neural networks how fast data can be handled in matrices (or arrays, with the numpy library in Python) compared to otherwise. Since then I have converted my fractal program back to single thread processing and now I calculate everything in matrices. Computation is 3x faster on a single thread than it ever was using multiple cores. And this is where I'm at now. I'm guessing the road ahead will have me learning how to do my matrix calculations on a GPU (when I get a new PC).

I know there's always the possibility of simplifying the math to make computations go faster, but my program takes a manual entry formula, (for example if I wanted to iterate Z^3 -1/Z + C^2) and I can't even imagine how to write code that can simplify arbitrary formulas on the fly.

Wait for more replies though. I tend to do things the hard way.

[rethread]

Gpus pack a giant bus if you want to go put your procedural generation code in shaders, but it only goes full speed if you keep your texture reads nice and small and repetitive.
Im not a big optimizer, i code the laziest stuff before i run it on the video card,  it goes pretty good, but if u had a decent optimization/simplification it would run faster on the faster. Thats tend to be my pattern of development,  aligning stuff to run on matrices sounds like something id try to do as well,  no maths simplification just trying to blockize the compute instead,  and just keeping the lazy....

[tsl]

Scratch will always be slow, it's interpreted language. 3 years ago I've made fractal flames explorer. It was my biggest Scratch (partly generated from Groovy scripts) project and I'm really happy with the result. In turbo mode it's fast enough for me. Check out: https://scratch.mit.edu/projects/17114670/
Phosphorus differently renders points and visually it's worse.
Give link to your sketch I can try to see if anything can be optimized.