Popcorn fractal is being implemented soonly. Next up after is Tetration Fractal. Paul Bourke did released a code, but I don’t know what to make of the complex2polar. I’ll ask @David_Tschumperle what does complex2polar implies?
//h file
typedef struct {
double x,y;
double r,t;
} COMPLEX;
COMPLEX ComplexPower(COMPLEX,COMPLEX);
COMPLEX ComplexTetration(COMPLEX,int);
COMPLEX ComplexTetration2(COMPLEX,int);
void Complex2Polar(COMPLEX *);
void Complex2Cart(COMPLEX *);
double ComplexModulus(COMPLEX);
double RealTetration(double,int);
//c file
/*
Recursive definition for tetration
*/
COMPLEX ComplexTetration(COMPLEX a,int n)
{
COMPLEX b,unity = {1,0,1,0};
if (n < 0) // Actually this is improper, tetration is only defined for n >= 0
n = -n;
if (n == 0)
return(unity);
b = ComplexPower(a,ComplexTetration(a,n-1));
return(b);
}
/*
Iterative definition for tetration
*/
COMPLEX ComplexTetration2(COMPLEX a,int n)
{
int i;
COMPLEX b,unity = {1,0,1,0};
if (n < 0) // Actually this is improper, tetration is only defined for n >= 0
n = -n;
if (n == 0)
return(unity);
b = a;
for (i=0;i<n;i++)
b = ComplexPower(a,b);
return(b);
}
/*
Complex power of a complex number
*/
COMPLEX ComplexPower(COMPLEX w,COMPLEX z)
{
COMPLEX d;
d.r = pow(w.r,z.x) * exp(-z.y * w.t);
d.t = z.y * log(w.r) + z.x * w.t;
Complex2Cart(&d);
return(d);
}
void Complex2Polar(COMPLEX *a)
{
a->r = sqrt(a->x*a->x + a->y*a->y);
a->t = atan2(a->y,a->x);
}
void Complex2Cart(COMPLEX *a)
{
a->x = a->r * cos(a->t);
a->y = a->r * sin(a->t);
}
/*
Recursive definition for tetration
*/
double RealTetration(double a,int n)
{
double b;
if (n < 0) // Actually this is improper, tetration is only value for n >= 0
n = -n;
if (n == 0)
return(1);
b = pow(a,RealTetration(a,n-1));
return(b);
}
double ComplexModulus(COMPLEX z)
{
double m;
m = sqrt(z.x*z.x + z.y*z.y);
return(m);
}
