Tiling using Spiral Hexaskelions

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.25.

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = golden ratio ~ 0.618.

The spirals are Archimedean spirals.

(1 < number of spiral turns < 2)

The spirals are Archimedean spirals.

(2 < number of spiral turns < 3)

The spirals are logarithmic spirals:

r(θ) = a exp(bθ), b = 0.05, 0.1, 0.15, 0.2, ..., 0.8.

( Mathematical software used: GeoGebra )

Spiral Starfish - a logarithmic spiral pentaskelion (螺旋海星)

A pentaskelion with five logarithmic spirals r(θ) = a*exp(b*θ),

b ~ 0.30635 (same as that of the golden spiral).

b = 0.25

b = 0.5

b = golden ratio ~ 0.618

( Mathematical software used: gnuplot )

Grid Art using Equations and Inequalities

(Monster)

(Funny Face)

(Monkey Face)

( Mathematical software used: Graph )

Flower of Golden Triangle Spirals (黃金三角螺旋花)

The Graph file used for this post can be found here.

( Mathematical software used: Graph )

Double Spirals - images of nested regular polygons under conformal mappings

(n = 6, Draw type = Lines)

(n = 4, Draw type = Dots)

These are images of nested regular polygons (n=6 & n=4)

under the Mobius transformation z -> 3(z-1)/(z+1).

( Mathematical software used: Graph )