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Not quite sure it's famous.  Maybe I'm too modest.

The new fractal does look interesting.  It's like finding a whole new family of fractals that were there all the time, but just needed discovering.

Hi Kalles Fraktaller and Simon,

I added SimonBrot2 to ManpWIN and include fractional powers of z from 3/2 upwards:

/**************************************************************************
   Run SimonBrot type fractals
   z^n * |z|^2 + c       (normal)
   z^n * |z^2| + c       (SimonBrot2)
**************************************************************************/

int   DoSimonSnakeFormula(void)

    {
    Complex   zabs, tempz, sqrtz;

    if (param[3] == 0.0)         // normal SimonBrot
   {
   zabs.x = fabs(z.x);
   zabs.y = fabs(z.y);
   tempz.y = z.y * zabs.x + z.x * zabs.y;
   tempz.x = z.x * zabs.x - z.y * zabs.y;
   sqrtz = (degree % 2 == 1) ? CSqrt(z) : 1.0;      // use square root power if degree is odd
   z = CPolynomial(tempz, degree / 2) * sqrtz + q;
   }
    else               // SimonBrot 2
   {
   tempz = z*z;
   zabs.x = fabs(tempz.x);
   zabs.y = -fabs(tempz.y);
   tempz = zabs;
   sqrtz = (degree % 2 == 1) ? CSqrt(z) : 1.0;         // use square root power if degree is odd
   z = CPolynomial(z, degree / 2) * sqrtz * tempz + q;
   }
    return (CSumSqr(z) >= rqlim);
    }

Here is SimonBrot2 z = z^n*|z^2|+c where n = 3/2



Here is a little Celtic Julia Animation I made using ManpWIN just for fun



It follows the path through Celtic as shown here in white:



Enjoy.