First 11 Expansions of the Dragon Curve Grammar

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Order 0 String

FX

Order 1 String

X+YF+

Order 2 String

X+YF++-FX-Y+

Order 3 String

X+YF++-FX-Y++-X+YF+--FX-Y+

Order 4 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+

Order 5 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

Order 6 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

Order 7 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

Order 8 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

Order 9 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

Order 10 String

X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--
X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-F
X-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+
YF+--FX-Y++-X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-
Y+--X+YF++-FX-Y+--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF
++-FX-Y+--X+YF+--FX-Y++-X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+
--X+YF+--FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y++-X+YF++-FX-Y+--X+YF+-
-FX-Y+--X+YF++-FX-Y++-X+YF+--FX-Y+--X+YF++-FX-Y+--X+YF+--FX-Y+

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