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Author Topic: Mathematical formula for fractal tree  (Read 11826 times)
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Jules Ruis
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Posts: 209


Jules Ruis


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« on: October 24, 2006, 10:15:59 PM »

I got from Titia the next algorithm for making a fractal in the Fractal Explorer, but it is not clear for me what the mathematical formula is. For using in Fi the formula must be of a form like z=z^2 + c#.
In case of a fractal tree I use as formula: if (x#>0) then z=(z-1)/c#,  else z=(z+1)/conj(c#)

Who can help me?

Algorithm

// -declaration of the local temporary variables
  var T0,T1,T2,T3,T4,T5 : TComplex;
Begin                         
  // -"julia" flag           
  If julia Then begin         
  end;                       
                             
  // -initialization code     
  //  (first iteration)       
  If iter_number=1 Then begin
  end;                       
                             
  // write your formula here 
  //Z:=CAdd(CSqr(Z),C);  // mandelbrot
  // z*Fn1(z)+Fn2(z)/z+P1/C
  T1:=Z;
  FuncDisp(FN1,T1);
  T2:=Z;
  FuncDisp(FN2,T2);
  T1:=CMul(Z,T1);
  Z:=CDiv(T2,Z);
  T2:=CDiv(P1,C);
  Z:=CAdd(T1,Z);
  Z:=CAdd(Z,T2);
                             
  SetResult(x,y, Z);         
                             
  // user-defined bailout test:
  // uncomment and change next
  // lines if you want         
//If x*x+y*y>4 Then begin     
//   EndLoop:=True;           
//end;                         
End;


* Fractal Tree Titia.GIF (30.85 KB, 237x174 - viewed 4429 times.)

* Fractal-Tree-Jules.jpg (61.78 KB, 320x240 - viewed 1635 times.)
« Last Edit: October 24, 2006, 10:23:14 PM by julesruis » Logged

Jules J.C.M. Ruis
www.fractal.org
matera
Guest
« Reply #1 on: October 25, 2006, 03:53:38 AM »

I think this might help - the problem is that the formula is compiled and the programming language (Delphi) complicates things. I have not, alas, bothered to take motes and figure out how to translate the mess back. My formulae are of the "duhhh... let's throw something in here and see what happens" kind LOL
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alan2here
Guest
« Reply #2 on: October 25, 2006, 09:28:04 PM »

There is a julia seed to the mendlebrot with 1.5 power that looks verry much like this too.
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titia
Guest
« Reply #3 on: October 25, 2006, 09:59:37 PM »

I just posted the *.frs file of the fractal tree in the "rate my file", parameter section. If you want to get a tree with this formula you also need the settings. It's a Fractal Explorer file.

« Last Edit: October 25, 2006, 10:21:24 PM by titia » Logged
lycium
Fractal Supremo
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Posts: 1146



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« Reply #4 on: October 30, 2006, 07:55:30 AM »

There is a julia seed to the mendlebrot with 1.5 power that looks verry much like this too.

that's exactly what it is: the glynn set

reference: http://www.efg2.com/Lab/FractalsAndChaos/GlynnFunction.htm (efg labs has even been linked on these very forums: http://www.fractalforums.com/index.php?topic=77.0)
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Jules Ruis
Fractal Lover
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Posts: 209


Jules Ruis


WWW
« Reply #5 on: October 30, 2006, 01:05:51 PM »

Thanks for the Glenn set. I think I am on the right track now!

Jules.
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Jules J.C.M. Ruis
www.fractal.org
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