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Hi guys!
I am wondering if either z-->z/c²  or z-->z*c² will form anything fractal if fed with the right starting values.
And what happens if I set c to a fixed value and just change z?

I have no clue how I could check any of this or where to start researching. How do you google for a formula?!
Is there a program(preferrably freeware) that you can feed with your own formulas and play around to see if it generates any fractal images?

Any input is appreciated!

this nifty little proggy lets you enter your own color formulas and fractal formulas



main page...
English https://www.physcip.uni-stuttgart.de/pages/~phy11733/index_e.html
German https://www.physcip.uni-stuttgart.de/pages/~phy11733/

as I recall, it's a bit slow but the formula parser is really very cool, and the source code is available, not sure if there is a windows version 

thank you guys!
I tried xaos - obviously the formulas don't do anything special, all I get is a circle

Here's a Julia-type fractal based on Pieman's idea.  f(z) = (z^n+c)/(c^n+z), for n = -2.

FractInt (for all its failings) does a reasonable job with its built-in formula parser.

I admit I use it to play with ideas (even if I have no idea if they'll work - they usually don't) to try to find interesting things.  That's how I found my 'Simonbrot' that people have been exploring.

The only problem with it is that because it was a DOS program you have to load your favourite text editor (notepad anyone) and create a .frm file containing your formulas.

This can be saved anywhere but by default FractInt looks in its own folder first.  I think that may also be configurable.

If you go down that route let me know so I can see if there's any way to assist.

I made it in Ultra Fractal.  Here is the formula.  If you don't use Ultra Fractal, you should be able to read the code and figure it out for the program that you use.  The Mandelbrot version is trickier, since finding a critical point for beginning the iteration is not trivial.


rational-julia {
;
; from pieman597
; http://www.fractalforums.com/general-discussion-b77/t24459/msg95653/#new
;
; based on f(z) = (z^2+c)/(c^2+z)
; generalize to any power
;
init:
  complex bottom=(0,0)
  complex c=@julparam
  complex cton=c^@power
  complex top=(0,0)
  complex z=#pixel
loop:
  top=z^@power+c
  bottom=z+cton
  z=top/bottom
bailout:
  |z|<@bailout
default:
  title="rational julia"
  complex param julparam
    caption="julia parameter"
    default=(0,1)
  endparam
  complex param power
    caption="power"
    default=2
  endparam
  float param bailout
    caption="bailout"
    default=1000
  endparam
switch:
  type="rational-mandelbrot"
  power=power
  bailout=bailout
}

Hi Simon,

I notice in your message: "Re: Do z-->z/c² or z-->z*c² create a fractal « Reply #8 on: September 02, 2016, 09:55:04 PM »" that you talk about the function parser in FRACTINT.

I have a windoze program with an on-screen parser based on the FRACTINT library. You may find it useful for playing with fractal formulae rather than all that tedious mucking about in hyperspace using text files interpreted in a Dossy program

It's a rough and ready program, but I have fun:

http://www.deleeuw.com.au/download/SetupManpWIN.exe

If you actually decide to try it, press T and the direct formula parser is in the middle of the dialogue box.

Have fun.

Paul the LionHeart

Hi Simon,

The current version of ManpWIN (including SimonBrot) is 3.03a.

I hope you can get it. Let me know if you can't and we will find a way.

I tried to attach it to a message but got: "Your file is too large. The maximum attachment size allowed is 256 KB. "