Buffalo fractals

I found/made/altered some 3D formulas. Basically I took the "MandelbulbulbPower2Iteration" and added some absolute operations. The idea was to create some kind of 3D burning ship. This failed, but it gave a 3D fractal that looks like the Buffalo fractal from the Kalles Fraktaler software.

2D Buffalo rendered with Kalles Fraktaler:

source: http://jeroensnake.deviantart.com/art/Bufallo-fractal-510382307

3D sliced buffalo rendered with customized Mandelbulber v2.02:

The original piece of code from MB, the "MandelbulbulbPower2Iteration" fractal:

Code:

void MandelbulbulbPower2Iteration(CVector3 &z)
{
	double x2 = z.x * z.x;
	double y2 = z.y * z.y;
	double z2 = z.z * z.z;
	double temp = 1.0 - z2 / (x2 + y2);
	double newx = (x2 - y2) * temp;
	double newy = 2.0 * z.x * z.y * temp;
	double newz = -2.0 * z.z * sqrt(x2 + y2);
	z.x = newx;
	z.y = newy;
	z.z = newz;
}

This original code gives the classic mandelbulber power 2 (both views are combination of sliced and full, one view from -Y and one view from Z direction)

The variations of the Buffalo family come from adding the abs() operation to a combination of the last 3 lines of the code:

Code:

z.x = newx;
z.y = newy;
z.z = newz;

And another version was created by mistake, by adding the wrong c variable at the wrong place (or something);

Code:

double x2 = z.x * z.x;
double y2 = z.y * z.y;
double z2 = z.z * z.z;
double temp = 1.0 - z2 / (x2 + y2);
double newx = (x2 - y2) * temp;
double newy = 2.0 * z.x * z.y * temp;
double newz = -2.0 * z.z * sqrt(x2 + y2);
z.x = fabs(newx + c.x);
z.y = newy + c.y;
z.z = fabs(newz + c.z);

Variations give a lot of possible combinations. Some images rendered from this family of formulas:

All images above this line are on my DA gallery. The rest below are loose images uploaded to imgur, only to be found here.

Some are in julia mode.

{
double x2 = z.x * z.x;
double y2 = z.y * z.y;
double z2 = z.z * z.z;
double temp = 1.0 - z2 / (x2 + y2);
double newx = (x2 - y2) * temp;
double newy = 2.0 * z.x * z.y * temp;
double newz = -2.0 * z.z * sqrt(x2 + y2);
z.x = newx;
z.y = fabs(newy);
z.z = fabs(newz);
}

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thanks and see you perhaps in 10 years again

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it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval, thanks and see you perhaps in 10 years again

The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again