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Simonbrot variation

(http://nocache-nocookies.digitalgott.com/gallery/19/8851_14_07_16_3_34_45.jpeg)

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=19424

Here is a variation of the famous Simonbrot
Forumla is z = z²*|z²|+c
A little different compared to Simonbrot's formula z = z²*|z|²+c

This fractal is much more disconnected.
Will be included in the next version of Kalles Fraktaler, I am struggeling to get it being able to zoom beyond e300, I might give that up on this formula though...

(un-zoomed shaped shown in the upper left corner)

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.

In FractInt formula terms, the simonbrot is:

z = z * abs(z) followed by
z = z * z + c

I changed it to say:

z = z * abs(z) + c
z = z * z + c

And it produces something that looks more sparse, but a small amount of zooming reveals mandelbrot minibrots.

Anyone like to turn that into perturbation code for Kalles Fraktaler?  Anyone able to describe what it is doing?

Hopefully not too dissimilar to be doable.

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

(http://deleeuw.com.au/misc/Simon2_3.png)

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

(http://deleeuw.com.au/misc/CelticJulia.gif)

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

(http://deleeuw.com.au/misc/CelticPath.png)

Enjoy.