Thanks James
There are various methods for calculating these fractals, but some have their drawbacks - for example, there is the IIM method (Inverse Iteration Method), which uses the function f(z)-> sqrt(z-c), but this means that you can't get the colour, and can also lead to problems.
The method that I am using iterates the function until it either reaches an iteration limit (set to 255), or when the "norm" of the complex number (modulus/size if you will) exceeds a certain limit. And the colour of that particular point is determined by the number of iterations taken to exceed that value.
But, you've got to be careful with this, as there is only finite memory allocated to AutoCAD, and that will put a limit on the number of points that can be generated.
My last image pushes it close, with around 1,300,000 points, but to get better images I tend to increase the resolution first (so that image generation is quick), and when I have identified a spot on the image that might be interesting to "blow up", I set the relevant image coordinates, and then take the resolution down to around 0.005.
However, as you can probably guess, the upper bound on the number of calcs the computer has to perform is somewhere around:
((y_max - y_min) / y_Resolution) x ((x_max - x_min) / x_Resolution) x Iteration_Limit
So, for my example:
((1.7 - (-1.7)) / 0.005) x ((1.0 - (-1.0)) / 0.005) x 255 = 69,360,000 Calculations
But, they are so worth it
Glad you like it mate,
Lee