Carotid Function Fractal

So called "Carotid-Kundalini" curves of degree i are defined as

where i ranges from 1 upwards, and -1 <= x <= 1

Superimposing the Carotid-Kundalini curves up to some degree on top of each results in a seemingly self similar structure.

First 10 curves

First 20 curves

First 30 curves

Zooms

C Source

#include "stdio.h"
#include "stdio.h"
#include "math.h"

int main(int argc,char **argv)
{
   int i,n;
   double x,y,dx;

   if (argc < 3) {
      fprintf(stderr,"Usage: %s n dx\n",argv[0]);
      exit(0);
   }
   n = atoi(argv[1]);
   dx = atof(argv[2]);

   for (x=-1;x<=1;x+=dx) {
      printf("%g ",x);
      for (i=1;i<n;i++) {
         y = cos(i * x * acos(x));
         printf("%g ",y);
      }
      printf("\n");
   }
}

Extension to 3D

The Carodit functions can be extended into 3D in a number of ways, the one used here is as follows where a and b are scaling factors.

The first 10 curves

The second 10 curves