gallery

dan and the giant sphere

dan and the giant sphere

at a small hideaway in sonoma, california lives a metal sphere apparently about 7 feet in diameter, and hence about 22 feet around.

that's an interesting pattern on the surface. any guess as to how many little shapes cover the sphere? my hand fits through one of them.

3D star - top view

3D star - top view

starting with the outer red curve (a slightly wiggly circle), the curves change color as they march inward toward the center of curvature at each point.

the slight wobble is magnified, especially vertically, as the curves go from orange to blue-green.

simple loopy curve

simple loopy curve

this is the graph of the parametric equations:

x(t) = 7 Cos[t] + 5 Sin[2 t]
y(t) = 5 Sin[t] + 7 Cos[2 t]
z(t) = 10 Cos[2 t]

the set of points {(x, y, z),  0 ≤ t ≤ 2π} forms the curve (t is in radians).

the bounding box is shown for reference, whatever it refers to.

sidetracked loop

sidetracked loop

The loop is flanked by two parallel companion curves at equal distance along the normal direction. 

Complex of loops

Complex of loops

The red curve has spawned seven more curves, changing in color and form based on the outer loop.

loopy ladder

loopy ladder

The two outer loops have now been joined up by 60 blue rungs and fallen over a bit.

saddle traces

saddle traces

The base grid is moved up to the saddle by z = y^2 – x^2 + 5. Trace curves are shown for x = 1.0 (blue) and y = 0.5 (red).

loopy dingles

loopy dingles

a 3D loopy curve is adorned with parallel curves and lots of struts with a colored ball on the end of each one.