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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;

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)