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Hi,

Ever wanted to pass more than just the z value from a formula to a colouring in Ultra Fractal ?

Well here's a way to do it - it's not perfect as it's a bit restrictive, is a noticeable overhead if used too much and degrades the accuracy of the z value concerned when used and requires that both the formula and colouring concerned understand what's going on *but* when needs must....

This is what I've used for passing a bailout type from a formula to a colouring - (integer) range 0 to 200 (max. possible range as implimented below 0 to 255) - I used it to pass the bailout type as part of the initial z value (I wanted the colouring to know the bailout type before iterating because the colouring has separate options for divergent/convergent/periodic and knowing the bailout type first avoids calculating for all possibilities).

Formula:-

; store the bailout type in #z
    float m = abs(real(#z))/512.0 ; scale by 512
    if m<1e-200 ; make sure it's not zero (so that the log works)
      m = 1e-200
    endif
    m = m + (bailout+256)*2.0^(ceil(log(m)/log(2.0))) ; add 256 to value
    if real(#z)<0.0
      m = -m
    endif
    #z = m + flip(imag(#z))

Colouring:-

; recover the bailout type and original value of #z
    float m = abs(real(#z))
    int n = 2.0^ceil(log(m)/log(2.0)-9) ; -9 as 512 is 2^9
    int k = floor(m/n)
    m = 512.0*(m - n*k) ; scale by 512
    bailout = k - 256 ; remove the 256
    if real(#z)<0.0
      m = -m
    endif
    #z = m + flip(imag(#z))

Obviously you could do a similar thing to pass a different value as part of imag(z) - or reduce the loss of accuracy in the z value by splitting your extra value between real(z) and imag(z).

Note that the above allows passing a value from 0 to 255 which requires 256 adding to the value which means adjusting the real(z) value by 512 i.e. 2^9 hence the values used above.
For a range from 0 to (2^n)-1 you need to add 2^n to your value and scale by 2^(n+1).
Obviously it is possible to do it for reals instead of integers, you'd just have to convert them to integers of a given number of bits first and adjust the code to add your custom conversion float<>int.