Choice Ravings

i have no idea if anyone else has seen this before (someone probably has), but i think it's really cool!

this is somewhat of a halfway point between the mandelbrot set and the burning ship. the original burning ship fractal is the result of taking the mandelbrot set's equation ( z = z^2 + c; where z and c are complex numbers ), but using the absolute value of z instead ( z = |z|^2 + c ).

the result is this, a very pretty fractal that is quite well known:

while experimenting with my own fractal renderer i've been working on, i realized that i didn't have to absolutize the entirety of z. because it's a complex number, the real and imaginary portions are stored in separate variables, so i tried to see what happens if you only do one of them!

absolutizing the real half was very boring, it just mirrored the bottom half of the burning ship to the top. but the imaginary half created the duck!

visually, i think this is probably my favorite fractal! i am very surprised how unique it is to the burning ship despite being so closely related. here's a couple really pretty screenshots i took: