Question: How can I display the required double spiral using complexplot?

This worksheet attempts to implement figures in Section 3 of the book "Indra's pearls" by Mumford, Series and Wright using the  command complexplot.

The worksheet seems to display Figure 3.1 on page 63 accurately but fails to correctly display Figure 3.4 on page 67.

Can complexplot be coded to accurately display this figure?

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