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Published bySolomon Fletcher Modified over 9 years ago
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L-Systems Lindenmayer Systems Prusinkiewicz and Lindenmayer
Recursive branching structure Complex but constrained.
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Recursive Branching Structure
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Botany - structure Stems, roots, buds, leaves, flowers
Herbaceous or woody Dichotomous or monopodial Terminal bud or lateral bud Vegetative bud or flower bud Alernate, opposite, or whorled.
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Botany - growth influences
Lineage - age Cellular descent - nutrients and hormones Tropisms - e.g., phototropism, geotropism Obstacles - collision response: temporary or permanent.
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DOL-Systems Production rules: ai -> bi D - deterministic
0 - zero contextual systems (context-free) Axiom - initial string Parallel rewriting rules.
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Geometric Interpretation of String
Geometric replacement - replace each symbol of string with a graphic element - connectivity assumptions Turtle graphics - each symbol is a command to a drawing pen.
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Geometric Replacement - Example
A -> BCB B -> XX C -> TT Axiom: A A BCB XXTTXX
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Geometric Replacement
XXTTXX X: T: X X T T X X
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Turtle Graphics “drawing turtle” is controlled by symbols of string
Symbols read from string in left to right order State of turtle: position and direction: (x, y, a) Parameters - d: linear step size - d: angular step size.
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Turtle Graphics F Move forward a distance d while drawing a line. Its state will change from (x,y,a) to (x+d*cos a, y+d*sin a, a) f Move forward a distance d without drawing a line. Its state will change as above. + Turn left by an angle d. Its state will change from (x,y, a) to (x,y, a + d) - Turn right by an angle d. Its state will change from (x,y, a) to (x,y, a - d).
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Turtle Graphics - Example
A -> BCB B -> FF C -> TT T -> -F++F- Axiom: A BCB FFTTFF FF -F++F- -F++F- FF
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Turtle Graphics - Example
d: d: 45 degrees Initial state: (10,10,0) FF -F++F- -F++F- FF F F -F++F- -F++F- F F
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Bracketed L-Systems Brackets - push and pop states
- multiple types of brackets - brackets have attachment semantics X X [ XX ] { XX } X X
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Properties Can be recursive - reduce size based on branching level
- self-similarity under scale Attribute symbols: line length, width, color, etc. Database amplification Track string development => growth process.
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Non-Deterministic S -> F A F A -> [ + F B F ] F F F
F [ + F F F ] F F F F S -> F A F A -> [ + F B F ] A -> F B -> [ - F B F ] B -> F Axiom: S F [ + F [ - F F F ] F ] F
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Stochastic L-Systems S 1.0 -> F A F A 0.8 -> [ + F B F ]
B 0.4 -> [ - F B F ] B 0.6 -> F
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Context-Sensitive L-Systems
S -> F A T A>T -> [ + F B F ] A>F -> F F<B -> [ - F A F ] F<B >F -> [ - F A F ] T -> F
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Animating Plant Growth
Flexible movement of structure Changes in topology due to growth process Elongation of existing structures F -> FF F -> F1 F1 -> F2 F2 -> F3 F 3-> F4
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Parametric L-Systems S -> A(0) A(t) -> A(t+1)
A(t): t>=1.0 -> F
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Timed L-Systems Global time variable Local age value
(u0, b0) -> ( (u1,a1), (u2, a2), … , (un, an) ) Jump from terminal age to terminal age.
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Interacting with the Environment
Physical obstacles Wind Gravity Nutrients, moisture from soil Sunlight: length of day, shadows.
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Open L-Systems Mech and Prusinkiewicz Communication terms
- Request and transmit information w/ environment - Distribution of nutrients, sunlight, etc.
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L-Systems - Summary Branching structure, self-similarity
Controlled complexity , data base amplification Geometric replacement, Turtle graphics Non-deterministic, stochastic, context sensitive, timed, open Animation - dynamics of static structure - time-varying drawing parameters - topology changes - growth of individual elements.
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