Mark
Dow
Geek
art
Simple
recursive systems
and fractal patterns
2x2
2-symbol L-system self-symmetries
2x2
2-symbol L-system
self-symmetry
thumbail chart
2x2
2-symbol
L-system self-symmetry tiny thumbail chart
About
self-symmetries and their graphical representation
[To Do]
What
do the self-symmetry diagrams mean?
They
illustrate where the system
pattern as a whole reappears in part of the system pattern. [To Do:
Explain and show examples.]
Do the
self-symmetry
diagrams show all self-symmetries?
No,
only the first self-symmetries that
don't cross power of two boundaries. [To Do: Explain and show example.]
[If the first symbol appears in the
first rule, that
quadrant will be
self-similar to the global pattern.]
Notes
[To Do: Examples of the following.]
A first rule that is all black, such
that the second
rule is never reached, is not included as it is not a two symbol system.
One pattern is included twice, one the
inverse
(symbol interchange) of the other. While I don't count this as a unique
pattern, the system occurs is properly located in two spots.
The 0 -> [0,0,0,0], 1 ->
[1,1,1,1] system
never returns to symbol zero. The pattern is equivalent to its fixed
point after the first generation. But it is a proper unique system if
the evolution is considered.
[To Do: Alternating mirror and swap symmetries are not always
represented. For example the Stripes
system
global symmetry should be symbol exchange symmetric about the vertical
axis. The Thue-Morse
system alternates between
vertical symmetry and anti-symmetry.]
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