![intothecontinuum:
A 2-coloring of what results from playing connect-the-dots with the complex numbers zn, for 0 < n < 140, as z varies from ei2.9531 to ei2.96104.
Mathematica code:
ListAnimate[Table[ Graphics[ GraphicsComplex[ Table[ {-1^n*Sin[n*a], 1^n*Cos[n*a]}, {n, 0, 139}], Polygon[Table[i, {i, 1, 139, 1}]]], PlotRange -> .55, ImageSize -> 500],{a, 2.9531, 2.96104, .00026}]]](http://25.media.tumblr.com/tumblr_m3q7u9j9Hq1qfjvexo1_500.gif)
A 2-coloring of what results from playing connect-the-dots with the complex numbers zn, for 0 < n < 140, as z varies from ei2.9531 to ei2.96104.
Mathematica code:
ListAnimate[
Table[
Graphics[
GraphicsComplex[
Table[
{-1^n*Sin[n*a], 1^n*Cos[n*a]},
{n, 0, 139}],
Polygon[Table[i, {i, 1, 139, 1}]]],
PlotRange -> .55, ImageSize -> 500],
{a, 2.9531, 2.96104, .00026}]]
![intothecontinuum:
Mathematica code:
ListAnimate[ Table[Show[ Table[Graphics[ GraphicsComplex[ Table[ {-(.975 + .025*Mod[.5 t + .5 G, 1])^n*Sin[n*3.586], (.975 + .025*Mod[.5 t + .5 G, 1])^n*Cos[n*3.586]}, {n, 0, 416}], {Opacity[(G +(.3+ t) (-1)^G)], Polygon[Table[i, {i, 1, 416, 1}]]}], PlotRange -> .04, ImageSize -> 500], {G, {0, 1}}]],{t, 0, .95, .05}]]](http://25.media.tumblr.com/tumblr_m3q4x8qKaf1qfjvexo1_r2_500.gif)
Mathematica code:
ListAnimate[
Table[Show[
Table[Graphics[
GraphicsComplex[
Table[
{-(.975 + .025*Mod[.5 t + .5 G, 1])^n*Sin[n*3.586],
(.975 + .025*Mod[.5 t + .5 G, 1])^n*Cos[n*3.586]},
{n, 0, 416}],
{Opacity[(G +(.3+ t) (-1)^G)], Polygon[Table[i, {i, 1, 416, 1}]]}],
PlotRange -> .04, ImageSize -> 500],
{G, {0, 1}}]],
{t, 0, .95, .05}]]






