The fractal is rendered with power from -8 to +8 and then rotated to "vertical" format (y is exponent) and finally it is revolving around the exponent axis.

The code:

x2=xold*xold;
y2=yold*yold;
po=__powf((x2+y2), 0.5f*pwr);
at=pwr*atan2f(((yold<0)?-yold:yold), xold);
xnew=po*__cosf(at)+re;
ynew=-po*__sinf(at)+im;

https://youtu.be/F5UzljA030k

Linkback: https://fractalforums.org/fractal-movie-gallery/19/perpendicular-burning-ship-with-arbitrary-exponent/920/

Well done!

I have an idea:

I know that you can do the Perpendicular Mandelbrot and the Heart by either doing a hybrid of Mandelbrot/BS or by multiplying the fractal by some power of i.

Off the top of my head, I also know that a real Buffalo and imaginary of this fractal gives the Perpendicular Buffalo.

You could do the formula for a Buffalo fractal in the complex plane with abs(zⁿ) + z₀.

Actually, those pictures are entirely correct. If you're looking for a Buffalo that is the way you want it e.g. this image, you'll have to negate the imaginary side.

The image is here: https://softologyblog.wordpress.com/2016/09/18/custom-formula-editor-for-visions-of-chaos/