Function Repository Resource:

# DoyleSpiral

Plot Doyle spirals

Contributed by: Dieter Steemann
 ResourceFunction["DoyleSpiral"][p,q] plots Doyle spirals for values p spiral arms and q circles per spiral revolution.

## Details and Options

Doyle spirals are special logarithmic spirals of touching circles in which every circle is surrounded by a corona of six touching circles. A linear fractional transformation (or Möbius transformation) is applied to map such spirals (in particular, circle packings) into double spirals.
A logarithmic spiral starts at the origin and winds around the origin at an ever-increasing distance. The Möbius transformation z(z-1)/(z+1) maps the points (0,1,∞) of the real axis of the complex plane to the points (-1,0,1) on the real axis. Because Möbius transformations preserve circles, the result is a new circle packing in the shape of a double spiral centered at +1 and -1 on the real axis.
"GraphicType" can be any of:
 "Basic" a spiral with parameters P and Q "Moebius" a basic spiral under Möbius transformation "PQGraph" a spiral with elements along the P- and Q-axes in basic spiral

## Examples

### Basic Examples (1)

Plot a Doyle spiral:

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### Options (5)

#### ColorFunction (1)

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#### GraphicType (2)

Use "GraphicType""Moebius":

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Use "GraphicType""PQGraph":

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#### PlotStyle (1)

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#### Type (1)

Compare and contrast the possible options for "Type":

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## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.0.0 – 29 March 2019