Barnsley-Mobius easy tutorial
This tutorial shows you how to easily make a good image using Barnsley formulas in UF5. I will not take care of the coloring style, but only of the basic shape, I'm sure you are already able to get a good colouring by yourself using some tutorials around. :)
First of all, update the formula database; it can be useful for having new stuff available. ;)
Now open UF, then hit CTRL+N for a new file.
Go to "Public" fmla folder, then in LGN.UFM (it is my folder...) then choose "Barnsley customizer". (Another nice formula is "Pinski's Bar customizer" in the same folder).
Set maxiter=250 (more accuracy)
In formula tab, expand the "Settings" heading - just to tweak something... for example set Extern shift = (0,1) , f(c)=tanh, f(z)=cosh. Now adjust the strength of those deformations, set % of f,p = 4 and rho% = 12 - if you use too high values you can blow up the Barnsley effect so be careful...
If you like symmetrical effects, now open "Polygonal effects" and set Polygonal order = 2.
Now you have a "strange" basic shape and you are ready to explore his Julia set!
Hit F7 and go with the cursor around the fractal and seek a spot not too near to black areas (or else you will get a black mass... ). Use the small preview window to see what's going on. When you are ready click.
Now you have a Julia set, but it has a "geometric" look, with sharp angles and straight lines. I don't like much this regularity, so let's twist it a bit with mapping!
Add a new mapping (in the tab of the Julia set). Go to sdc.uxf and choose "Mobius toolbox". This mapping needs to be seen "from distance" so go in location tab and set magnification = 0.1
For now leave "Double spiral", normally it's good for almost anything. If you don't like it, try Cayley Map or Pairing Circles, but don't get discouraged... If you don't zoom in you don't see the best spots! Anyway for now I suppose that you leave default settings.
Change the settings of the mapping as follows;
ITERATIONS = 6, 7 or 8 (too much iters deform too much)
SCALE = (2,0)
Now choose fixed points as you like but opposite values, for example (1,0) and (-1,0) or (1,1) and (-1,-1) ... I can't tell the perfect ones because it depends to the actual fractal shape, try by yourself. (Maybe you like non opposite fixed points, I don't mind!)
EDIT. I have found that if you use SCALE = (1.23,0) you can use more iterations, so it's worth try this...
Zoom in again and find an interesting spot; now you will notice that the "cutting lines" are nicely curved and they form a decorative intricate pattern! :D Choose a good coloring and you will get some nice fractals with ease.
Have a nice day! Luca :D