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Some interesting patterns:

Flat spiral disc

12x12 granny square

Cylinder made by stitching a square together at two sides with single crochet

Larger surface of constant negative curvature

For this I used the formula from Daina Taimina's excellent book: each row has n stitches, where:

n = 2*pi*R*sinh(h*i/R)/w 

where R=2.0cm is the radius of curvature (controls the frilliness), h=0.55cm is the stitch height, w=0.55cm is the stitch width, i is the row number (1,2,3,...) and sinh() is the hyperbolic sine function.

Small sphere

Torus

Amusing error - I was trying a torus but got the coding very wrong! Consider this an example of the computer expressing its own creativity.