Visualize a geometric progression (GP) of your choice in a concrete manner that emphasizes the wide range of scales inherent to a GP. This is a simple exercise in Cartesian geometry that can look as mathy as you like, or not.

// the circles' radii are a geometric progression, one starting 
// with 4, another 3, and a third 2.  also, the colors the ciricles 
// are in are a geometric progression - 4, 16, 64

paper 0
load dbngraphics.dbn

// lightest circles, starts with radius 4
circle 0 0 4 4
circle 0 0 16 4
circle 0 0 64 4

// medium colored circles, starts with radius 3
circle 0 0 3 16
circle 0 0 9 16
circle 0 0 27 16
circle 0 0 81 16

// darkest circles, starts with radius 2
circle 0 0 2 64
circle 0 0 4 64
circle 0 0 8 64
circle 0 0 16 64
circle 0 0 32 64
circle 0 0 64 64
circle 0 0 128 64

// lines corresponding to darkest circles' edges
pen 50
line 2 0 2 100
line 4 0 4 100
line 8 0 8 100
line 16 0 16 100
line 32 0 32 100
line 64 0 64 100