oldz function

Note: This function is provided for backwards compatibility and should no longer be used. You can declare an array[#maxiter + 1] to store the values of #z, and process them in the final section of the coloring algorithm. This is more efficient and more flexible. See Function oldz is deprecated.

This function returns the z value belonging to the specified iteration. This function can only be used in the final section of a coloring algorithm. If it is used, the value of #z is stored after each iteration in the fractal formula, so it can be retrieved by the coloring algorithm afterwards. This allows the coloring algorithm to process the values of z in arbitrary order. The argument of the function is the iteration in which the desired z value was produced.

This piece of code shows how the z value is stored:

execute init section of fractal formula
oldz[0] = #z
int iter = 0
repeat
  execute loop section of fractal formula
  iter = iter + 1
  bool b = the expression in the bailout section of the fractal formula
  oldz[iter] = #z
until (b == false) || (iter == #maxiter)
#numiter = iter

The oldz function will only return valid z values if the argument is in the range 0..#numiter. Otherwise, (0,0) is returned. Here is an example of a coloring algorithm using oldz:

oldzexample {
final:
  int iter = 1
  ; initialize variables
  while iter <= #numiter
    the_z = oldz(iter)
    ; do something with the value of the_z
    iter = iter + 1
  endwhile
  ; color the pixel
}

This is equivalent to:

loopexample {
init:
  ; initialize variables
loop:
  ; do something with the value of #z
final:
  ; color the pixel
}

Here, you could better use the normal loop section instead of the oldz function, but some coloring algorithms need to process the values of z in non-linear order. In that case, you must use the oldz function, or an array.