END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

hi there, i like the attempt on ordering the alternating/hybrid generation of formulas, i recently used another method,
which is more like a biased alternate:

range - a integer value
bias - a integer value <range

and then for each iteration the test is

if(iteration%range>bias){
useFormulaA
}else{
useFormulaB
}

it is not perfect, i know, but it could produce sequences like
AAAAABBBBBB
AAAAAABBBBB
...


when seeing those "AB.." strings, i have to think about l-systems, to produce longer - and more complicated - rule sequences ...
it is all about, "how to define an endless formula lookup table"....

it is just a subset i know but it is only 3 lines of code to implement more variance when you only have 2 formulas

to understand what is possible, with alternation/hybrid methods, make sure you understand that once an iteration has been escaped its form wont change in further iterations, this is the reason why the "1st" formula defines the overall shape

this effect can be understood best if you define an iteration when to swith it, this way you could display a fractal in the "black" area of another, but it is not leading to that interesting effects



to your method:

you know you have limitations as well ?

e.g. for a 24 iteration the sequence

"AAAABBBB" would look like:
"AAAABBBBAAAABBBBAAAABBBB"

the sequences could grow bigger, but at the end you are just modulo+iterating over the chars in the string if your iteration exceeds the string length ....
so, i like the way to define some kind of language ( perhaps branching would also make sense ... ) similar to the LSYSTEMs
http://de.wikipedia.org/wiki/Lindenmayer-System

I could add additional transform sets to my software, I'll continue with the 2 set version for the time being as I've only just scratched the surface of this class of fractals. At the moment all my formulae are coded in C++ in the main body of the program, at some point I'll have to investigate how to incorporate some sort of fractal programming language along the same lines as UF, Fractal Science Kit and others.

cKleinhuls, do you have any example pictures using your technique?

there exist plenty of methods to create new formula ( e.g. spherical/polar interpolation of 2 different formula in one iteration )
adding/dividing/multiplying/subtracting is also easy to achieve and try out

you are right that implementing a hybrid in one single iter step leads to different results, i can imagine a formula editor that has checkboxes for each formula in the created hybrid that can be checked as ( bailout test ) so that "simple" formulas like adding/subtracting wouldnt lead to a bailout condition....  this way every form could be doable ...

i would love to see a drag&drop formula editor with simple operators to combine different fractal formula.... or create new ones

i would love to see a language that lets define a logic for at which iteration step wich formula to use ( similar ot the above "AAABAABA" style ) , i can think of many more hybrid options, like:
Base Formula would be A
"use formula X at Iteration Y"
"use formula X at Iteration Y1 to Y2"
"use formula X at every nth Iteration"
"if |z|<Y use formula X else use formula X2"


... and so on, some of these hybrids are available in my ultrafractal formula collection

remember that each formula can have its own variable settings...


in fact you could define a different formula at each iteration, but this would certainly lead to crappy results


gotta open up ultra fractals formula editor now ....

This is a good idea !
Don't forget that by doing this you are just changing the initial formulae : if you are doing AB with A: "z^2+c" and B: "z^2-c" it is just like iterating over "(z^2+c)^2-c".
Great images btw.

It might be an option to use algorithmically specified sequences instead of fixed strings consisting of A and B. These can be aperiodic, and so avoid the problem that one really just iterates a larger, composited, function. For example the Thue-Morse-Sequence: http://en.wikipedia.org/wiki/Thue–Morse_sequence .