This GT is based on the Gumowski-Mira chaotic attractor.
A particular variant was called "Mythic Bird" due to its similarity to feathered wings.

The code to generate this is minimal:

X=0.01,Y=0
G=()=>M*X+2*(1-M)*X*X/(1+X*X)
for(I=N;I>0;I--)
{
plot(W/2+X*SCALEX,H/2+Y*SCALEY)
Z=X,X=Y+G()+A*(1-B*Y*Y)*Y,Y=-Z+G()
}

The co-efficients A, B and M decide the final shape.

In this version, M is selected randomly from a set of known values, and it generates wings, blobs, oil slicks, and various other organic shapes.