intothecontinuum:

The catenoid and helicoid are isometric. Meaning one can be transformed into the other without changing the distance between any of the points. 
(via lickycat)
intothecontinuum:

Mathematica code:
 Animate[   Graphics[     Table[       Circle[{30*Cos[i*Pi/4], 30*Sin[i*Pi/4]},        t + (50 - n) (1 + Sign[50 - n])/2],     {n, 0, 50, 1}, {i, 0, 7, 1}],   PlotRange -> 12, ImageSize -> 500], {t, 0, 1, .1}]
dvdp:

111109
intothecontinuum:

Mathematica code:
v1 := {1 + Cos[Pi/3], Sin[Pi/3]}
v2 := {0, 2 Sin[Pi/3]}

Animate[
  Graphics[
     Table[Rotate[Table[{PointSize[.025],
        Point[
          Table[           {Cos[n*2*Pi/6], Sin[n*2*Pi/6]} + m1*v1 + m2*v2,
          {n, 0, 5}]]},
     {m1, -15, 15}, {m2, -15, 15}], t*o], {o, 0, 1, 1}],
  PlotRange -> 15, ImageSize -> 500],{t, 0, Pi/3, Pi/60}]
greyfaced:

bass
by: grey faced
intothecontinuum:

Hi-res (700x700):
r = 1
2.35664 ≤ a ≤ 2.35773
s = 320
Mathematica code:
Manipulate[Graphics[Line[   Table[{-r^n*Sin[n*2*Pi/a], r^n*Cos[n*2*Pi/a]}, {n, 0, s}]],  PlotRange -> 1.3], {r, .1, 1}, {a, 0.001, 4*Pi, .00005}, {s, 1, 800, 1}]