December 2007
The patch from figure 14 contains decagons and pentacles divided up as follows:
![](/issue45/features/kaplan/subs_rules2.gif)
Each of these two substitutions introduces rhombi. These can be swallowed up by the two new shapes introduced here:
![](/issue45/features/kaplan/swallow_rhombi.gif)
This substitution turns the patch on the left (the original figure 14) into the patch on the right (our new figure 20):
![](/issue45/features/kaplan/compare_swallow.gif)