Symmetric patterns for Pygram

by Helmut Postl

I think, there are too many to list all of them Here I will show some
general constructions how to build symmetric patterns.

Double subpatterns

We want to construct a set of small patterns which can be filled exactly
twice by all pygram pieces. For example:

These three subpatterns can be put together in *any way* (there are
lots!) to make a “half-pattern”, for example:

One of the two copies of this half-pattern is flipped over, and then the two
half-patterns can be arranged in several ways to make a symmetric whole
pattern (here the first example is used):

Here are more examples for double subpatterns:

Double subpatterns with symmetric
subpattern

Another way to construct symmetric patterns is to use
a small symmetric subpattern which comes to lie on the axis of symmetry. The
double subpatterns are arranged symmetrically as above. For example:

Again, the two subpatterns can be put together in *any way* to make a
“half-pattern”, for example:

Again, one of the two copies of this half-pattern is flipped over, and then
the two half-patterns can be arranged in several ways with the symmetric
subpattern to make a symmetric whole pattern (again, the first example is
used):

Here are more examples for double subpatterns with symmetric subpattern:

Wat is het toch plezant om slimme vrienden te hebben. Bedankt Helmut!