Potential in dynamical plane = CPM/J





To be true :
- interior of Kc should be black ( potential =0 ) but then image looks boring.
- To remove repetition of gray gradient ( if potential>1 then 255*potential>255 ) do :

temp=255*potential;
if (temp>255)
color=255;
else color= temp;



Here you can see logphi along real axis for c=0. Here Julia set is unit circle.



As you see potential is real number :
* equal to 0 inside Kc
* positive outside Kc

So in pseudocode :
if (LastIteration==IterationMax)
then potential=0 /* inside Filled-in Julia set */
else potential= GiveLogPhi(z0,c,ER,nMax); /* outside */



Comparisen of 2 definitions of potential : full and simple :






How to change smooth potential to discrete level sets :




Here level sets of potential are seen (pLSM/J).

potential=jlogphi(Zx, Zy,Cx,Cy);
temp=floor(log2(255*potential)); // temp is int
// checking odd and even
if (temp % 2==0) color= 255;
else color=0;
array[((iYmax-iY-1)*iXmax+iX)]= color ;


Boundaries of level sets of potential are equipotential curves.
External rays ( field lines of complex potential ) are perpendicular to equipotentials ( are gradient lines)


Boundaries of level curves of potential are equipotential lines.



here is c code for coputing point of equipotential curve :

potential=jlogphi(Zx, Zy,Cx,Cy);
Level=floor(log2(255*potential));
/* plot point of Level Curve */
if (iX!=0 && Level!=PreviousLevel)
{
array[((iYmax-iY-1)*iXmax+iX)]=0;
PreviousLevel=Level;
}





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Autor: Adam Majewski

Feel free to e-mail me. (:-)) adammaj1-at-o2-dot--pl

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