Pretty sure it shows a 'stack' of 2D Julia set representations, so yes the top surface is a horizontal plane.
I think it looks non-flat because the whorls resemble slightly distorted ellipses, which you perceive as circles slightly tilted or curved with respect to the top plane/each other.
Is the 'face' of this a flat surface? It doesnt look it to me. If not, why not?
1 Attachment