Global sections
Sometimes, initializing variables of a formula can require a large number of calculations. Since you would normally initialize variables in the init section of a fractal formula or a coloring algorithm (or the transform section of a transformation), these calculations are performed again and again for every pixel.
Often, they only depend on parameter settings, and therefore the results are the same for every pixel. To avoid doing many repeated calculations, you can move them to the global section. This is a special section at the start of a formula that is executed once per image.
Use the global section to perform per-image calculations and store the results in variables that can be read in other sections. Variables declared here are treated as read-only in other sections, so you cannot use this to share variables across pixels (that would not work reliably).
In the following example, the global section is used to pre-calculate an array of random values that is the same for every pixel. These random values are subsequently used to disturb a standard Mandelbrot set.
MandelbrotModified { global: float values[#maxiter] int i = 0 int seed = 12345678 while i < 100 seed = random(seed) values[i] = seed / #randomrange i = i + 1 endwhile init: z = (0,0) int iter = 0 ; "i" is already taken loop: z = sqr(z) + #pixel + values[iter] iter = iter + 1 bailout: |z| 4 }
Notes
- Global sections are often combined with arrays to compute look-up tables that can speed up the formula tremendously.
- You can even declare an array equal to the size of the image (with the #width and #height predefined symbols) and calculate the entire fractal in the global section of a coloring algorithm. The final section is then used only to return colors or index values from this array. This enables you to implement fractal types like IFS and flame fractals that are not natively supported by Ultra Fractal. This technique does have some limitations: it can require a fair amount of memory and the progress of the calculation is not reported. It is very slow and memory-intensive with rendering to disk, especially with anti-aliasing, and it does not work well with network calculations either. See also the render setting.
Next: Image parameters