In general, it's probably easier to fiddle with the examples than it is to get everything from the help. But a couple things the examples don't necessarily tell you. Each line is a command. Lines starting # are comments. // can be used to comment the remainder of a line. Commands are executed in order, so if you want a coloured circular background, you need to set the Radius first so that the circle is the correct radius, then call Background so it sits under the remaining graphics, and then call Ticks. It also means you need to start with the biggest circle first.
The simplest example, demonstrating the very basics
Radius 300
Formula log(#)
Ticks 1: 1.2: 1.4: 1.6: 1.8: 2: 2.5: 3: 3.5: 4: 5: 6: 7: 8: 9: 10
XLabels 9.7:C
XTicks pi:π
load simplest
A basic example, demonstrating some things that can be done
Textstyle font-size:6pt;text-anchor: end;
Textdrop 12
TextAngleOffset -0.3
LineStyle stroke:black;stroke-width:0.7;
Spacing 2
Front
# C
Radius 300
Formula log(#)
Background aliceblue
Ticks 1: 1.2: 1.4: 1.6: 1.8: 2: 2.5: 3: 3.5: 4: 5: 6: 7: 8: 9: 10
XLabels 9.7:C
XTicks pi:π
# CF
Radius 280
Formula log(x/pi)
Background white
Ticks 3: 4: 5: 6: 7: 8: 9: 10: 12: 15: 20: 25: 30
XLabels 3:CF
XTicks pi:π
# T
Radius 260
Background aliceblue
Formula log(tan(#))
Ticks 5.7 6: 7: 8: 9: 10: 12: 14: 16: 18: 20: 25: 30: 35: 40: 45
XLabels 5.7:T
# S
Radius 240
Background white
Formula log(sin(#))
Ticks 5.7 6: 7: 8: 9: 10: 12: 14: 16: 18: 20: 25: 30: 35: 40: 45: 50: 60: 70: 80],
XLabels 5.7:S
# ST
Radius 220
Background aliceblue
Formula log(sin(#/10))
Ticks 0.57 0.6: 0.8: 1: 1.2: 1.5: 2: 3: 4: 5: 5.7
Xlabels 5.7:ST
# CI
Radius 200
Background white
Formula -log(#)
Ticks 10 9: 8: 7: 6: 5: 4: 3: 2: 1.5: 1.2 1
XTicks pi:π
XLabels 1:CI
# B
Radius 180
Background aliceblue
Formula log(sqrt(#))
Ticks 1 1.2 1.5: 2: 3: 4: 5: 6: 7: 8: 10: 12 15: 20: 30: 40: 50: 60: 70: 80: 100
XLabels 1:B
# K
Radius 160
Background white
Formula log(pow(#,1/3))
Ticks 1 2: 5: 10: 20: 50: 100: 200: 500: 1000
XLabels 1:K
# L
Radius 140
Background aliceblue
Formula #
Ticks 0 0.1: 0.2: 0.3: 0.4: 0.5: 0.6: 0.7: 0.8: 0.9: 1
XLabels 0:L
Textstyle font-size:6pt;text-anchor: middle;
Textdrop 20
TextAngleOffset 0.3
# LL
Radius 120
Background white
Formula log(log(#))
Ticks 10 20: 50: 100: 1000: 1e4: 1e5 1e6: 1e7 1e8: 1e9 1e10
XLabels 0:LL
basic