This lecture continues our consideration of L-Systems and morphogenic processes.

1. Use L-system to generate turtle commands. Basis for simple, stylized plants.
2. Some exercises to think about (some in lab):
   1. Draw an oriented line.
   2. Draw a triangle.
   3. Draw a square.
   4. Draw like Spirograph! How?
   5. Draw a simple snowflake.
   6. Can you draw a binary tree without intersecting branches?
   7. Draw a simple tree.
   8. Draw a more complex tree.
   9. Draw an aperiodic comb.
   10. Draw a fractal snowflake.
   11. What do we get with the following grammar?
       1. Start: FX
       2. All turns 90 degrees.
       3. X → X+YF+
       4. Y → -FX-Y
3. Fractal dimension: log(self-similar pieces)/log(magnification).
4. Today's lab.
   1. Handed out today, please return in mailbox or electronically next Tuesday, in class.
   2. No scheduled lab (I have a scheduling conflict), but I'll hold office hours tonight (11/16) 8-9, and I'll be in next Monday, 9-noon, and 2-4.
   3. Hints on determining scaling factors.
5. Other important applications of L-systems:
   1. The generation of Kolam patterns: an old artistic practice in southern India.
      1. Continuous lines or cycles drawn about a matrix of points.
      2. Complexity of hand-drawn patterns signifies the importance of the day. The most complex patterns may take up a length of street.
      3. Patterns handed down, often orally, from generation to generation. In some cases, rhymes or chants are used to help direct the drawing of pattern. Complexity of pattern is mirrored in the complexity of song (see below).
      4. Context sensitive cycle-grammars, based on L-systems, can be used to model these structures.
   2. Song structure. See an important and silly paper by Don Knuth. Viz. "That's the way, uh huh, I like it!"
   3. Structure of massively parallel programs. Parallel-rewriting systems support the development of massive regular structures in high-performance systems.
6. Morphology.
   1. Turing's approach: think of a living system as having continuous interactions between components that guide the development of simple patterns.
   2. Early structure development in Drosophila; how does banding happen?
   3. We now know that the development of these features are governed by gene expression.
   4. A similar mechanism seems to guide the structuring of the brain. Still, the growth of neurons and placement of synapses has "run-time" and environmental components (see Marcus, below).
   5. Work by Prusinkiewicz (see below) on virtual botany and developmental morphology in plants.
7. Next week: puzzles and problems.

Resources needed for this class:

• The L-system applet.
• A wonderful kolam website.
• The Algorithmic Botany website, by the Prusinkiewicz research group.
• For Thursday's lecture, Turing's A Chemical Basis for Morphogenesis. This reading is difficult, at best, but a skimming will give a sense of Turing's skill at approaching a diversity of problems.
• Donald Knuth's paper on song complexity.
• Work by Wieschaus and Nusslein-Volhard demonstrate that developmental morphology of Drosophila once thought controlled by morphogens has, in fact, a genetic component.
• The Birth of the Mind by Gary Marcus. "How a tiny number of genes creates the complexities of human thought."

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