Few spirals are as beautiful as the Harriss spiral.

to curve :length
  pu
    lt 45
    fd :length/2 * sqrt(2)
    rt 90
  pd
  penwidth :length/15
  arc :length/2 * sqrt(2) 90
  pu
    fd :length/2 * sqrt(2) lt 90
    lt 45
    rt 90
  pd
end
to harriss :length :limit
if :length > :limit
[
  color [200 - :length  0 128 - :length/3]
  curve :length
  rt 90
  harriss :length/2.325 :limit
  lt 180
  harriss :length/1.325 :limit
  rt 90
  pu
  back :length
  pd
] 
end
harriss 300 5

But I think if you replace the number 2.325 and 1.325 with other numbers you get interesting spirals.

The Hairy Harriss

Here's what we get if we go with the golden ratio and 1.325.

to curve :length
  pu
    lt 45
    fd :length/2 * sqrt(2)
    rt 90
  pd
  penwidth :length/15
  arc :length/2 * sqrt(2) 90
  pu
    fd :length/2 * sqrt(2) lt 90
    lt 45
    rt 90
  pd
end
to harriss :length :limit
if :length > :limit
[
  curve :length
  rt 90
  harriss :length/1.618 :limit
  lt 180
  harriss :length/1.325 :limit
  rt 90
  pu
  back :length
  pd
] 
end
harriss 300 5

External Links

• The golden ratio has spawned a beautiful new curve: the Harriss spiral
• Edmund Harriss' Blog