lindenmayer systems

axi/__init__.py

@@ -1,5 +1,6 @@
 from .device import Device
 from .drawing import Drawing
+from .lindenmayer import LSystem
 from .paths import simplify_paths, sort_paths, join_paths, load_paths
 from .planner import Planner
 from .turtle import Turtle

axi/lindenmayer.py

@@ -0,0 +1,53 @@
+import random
+import re
+
+from math import sin, cos, radians
+
+from .drawing import Drawing
+
+class LSystem(object):
+    def __init__(self, rules):
+        self.rules = rules
+        self.pattern = re.compile('|'.join('(%s)' % x for x in rules))
+
+    def step(self, value):
+        def func(match):
+            rule = self.rules[match.group(0)]
+            if isinstance(rule, basestring):
+                return rule
+            return random.choice(rule)
+        return self.pattern.sub(func, value)
+
+    def steps(self, value, iterations):
+        for i in range(iterations):
+            value = self.step(value)
+        return value
+
+    def run(self, start, iterations, angle=None):
+        program = self.steps(start, iterations)
+        angle = angle and radians(angle)
+        state = (0.0, 0.0, 0.0)
+        stack = []
+        paths = []
+        point = (0.0, 0.0)
+        for instruction in program:
+            x, y, a = state
+            if instruction == '-':
+                a -= angle
+            elif instruction == '+':
+                a += angle
+            elif instruction == '[':
+                stack.append(state)
+            elif instruction == ']':
+                x, y, a = stack.pop()
+                point = (x, y)
+            else:
+                x += cos(a)
+                y += sin(a)
+                if paths and point == paths[-1][-1]:
+                    paths[-1].append((x, y))
+                else:
+                    paths.append([point, (x, y)])
+                point = (x, y)
+            state = (x, y, a)
+        return Drawing(paths)

examples/lindenmayer.py

@@ -0,0 +1,21 @@
+import axi
+
+def main():
+    system = axi.LSystem({
+        'A': 'A-B--B+A++AA+B-',
+        'B': '+A-BB--B-A++A+B',
+    })
+    d = system.run('A', 5, 60)
+    # system = axi.LSystem({
+    #     'X': 'F-[[X]+X]+F[+FX]-X',
+    #     'F': 'FF',
+    # })
+    # d = system.run('X', 6, 20)
+    d = d.rotate_and_scale_to_fit(12, 8.5, step=90)
+    # d = d.sort_paths()
+    # d = d.join_paths(0.015)
+    d.render().write_to_png('out.png')
+    axi.draw(d)
+
+if __name__ == '__main__':
+    main()