Orthocircles

orthocircles morph 001
The union of the three unit circles in the coordinate planes is the minimum set of the degree 6 polynomial, that has the surfaces of this animation as level sets.

The Ortho Circles Surface is defined as:

((x^2 + y^2 - 1)^2 + z^2)*((y^2 + z^2 - 1)^2 + x^2)*((z^2 + x^2 - 1)^2 + y^2) - ff^2*(1 + bb*(x^2 + y^2 + z^2))

orthocircles borromean  001
Borromean of ortho-ellipses. In this animation the minimum set of a polynomial function is changed from three intersecting circles to three ellipses which form a Borromean link.
orthocircles singular
Borromean of ortho-ellipses. The singular level has 12 conical singularities.
orthocircles flow 001
orthocircles flow (anaglyph)
This animation shows how the points of the first image move along the gradient lines of the function to the minimum set, the three unit circles in the coordinate planes.

ImplicitCompact.pdf