Copyright	(c) 2015 Jeffrey Rosenbluth
License	BSD-style (see LICENSE)
Maintainer	jeffrey.rosenbluth@gmail.com
Safe Haskell	None
Language	Haskell2010

Diagrams.TwoD.Path.LSystem

Contents

Lindenmayer Systems
Predefined L-Systems
Re-exports from Diagrams.TwoD.Path.Turtle

Description

Create LSystem diagrams and paths.

See "The Algorithmic Beauty of Plants". http://algorithmicbotany.org/papers/abop/abop-ch1.pdf

Synopsis

Lindenmayer Systems

L-Systems

data Symbol n Source #

Symbols:

```
F ('F') draw a segment.
```

G ('f' or 'G') move the turtle one unit without drawing anything.

```
Plus ('+') turn the turtle clockwise.
```

Minus ('-') turn the turtle anti-clockwise.

Reverse ('!') turn the turtle 180 degrees.

```
Flip ('~') switch right and left.
```

Push ('[') push the current state onto the stack.

```
Pop (']') pop the current state.
```

Width x ('<', '>') increase (decrease) stroke width by factor of 1.1 (0.9).

Delta x ('(', ')') increase (decrease) turn angle by factor of 1.1 (0.9).

```
X n ('X','Y','Z','A','B') constants.
```

Constructors

F
G
Plus
Minus
Reverse
Flip
Push
Pop
X Int
Width n
Delta n

Instances

Eq n => Eq (Symbol n) Source #
Methods (==) :: Symbol n -> Symbol n -> Bool # (/=) :: Symbol n -> Symbol n -> Bool #
Ord n => Ord (Symbol n) Source #
Methods compare :: Symbol n -> Symbol n -> Ordering # (<) :: Symbol n -> Symbol n -> Bool # (<=) :: Symbol n -> Symbol n -> Bool # (>) :: Symbol n -> Symbol n -> Bool # (>=) :: Symbol n -> Symbol n -> Bool # max :: Symbol n -> Symbol n -> Symbol n # min :: Symbol n -> Symbol n -> Symbol n #
Show n => Show (Symbol n) Source #
Methods showsPrec :: Int -> Symbol n -> ShowS # show :: Symbol n -> String # showList :: [Symbol n] -> ShowS #

type Rules n = Map (Symbol n) [Symbol n] Source #

Production rules.

generations :: Ord n => Rules n -> [Symbol n] -> [[Symbol n]] Source #

Successive generations of the production rules applied to the starting symbols.

L-System graphics

lSystemR :: (Floating n, Ord n) => [Symbol n] -> Reader (Environment n) (TurtleState n) Source #

Interpret a list of symbols as turtle graphics commands to create a TurtleState. The turtle data is tracked in a Reader monad.

lSystem :: (Floating n, Ord n) => Int -> Angle n -> [Symbol n] -> Rules n -> TurtleState n Source #

Create a TurtelState using n iterations of the rules with given axiom symbols and the angle increment, delta. The first segment is in the unitX direction.

lSystemPath :: (Floating n, Ord n) => Int -> Angle n -> [Symbol n] -> Rules n -> Path V2 n Source #

Create a path using n iterations of the rules with given axiom symbols and the angle increment, delta. The first segment is in the unitX direction. The styles in the TurtleState are ignored.

lSystemDiagram :: (TypeableFloat n, Renderable (Path V2 n) b) => Int -> Angle n -> [Symbol n] -> Rules n -> QDiagram b V2 n Any Source #

Create a diagram using n iterations of the rules with given axiom symbols and the angle increment, delta. The first segment is in the unitX direction. The styles in the TurtleState are applied to the trails in the diagram.

Making rules from strings

symbol :: Fractional n => Char -> Symbol n Source #

symbols :: Fractional n => String -> [Symbol n] Source #

rule :: Fractional n => Char -> String -> (Symbol n, [Symbol n]) Source #

Predefined L-Systems

sierpinski :: RealFloat n => Int -> TurtleState n Source #

Sierpinski triangle.

cantor :: (Renderable (Path V2 n) b, TypeableFloat n) => Int -> QDiagram b V2 n Any Source #

Cantor dust

dragon :: RealFloat n => Int -> TurtleState n Source #

Dragon curve

hexGosper :: RealFloat n => Int -> TurtleState n Source #

Hexagonal Gosper curve

kochIsland :: RealFloat n => Int -> TurtleState n Source #

Koch Island

kochLake :: RealFloat n => Int -> TurtleState n Source #

Koch lake

koch1 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 1

koch2 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 2

koch3 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 3

koch4 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 4

koch5 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 5

koch6 :: RealFloat n => Int -> TurtleState n Source #

Koch curve 6

tree1 :: RealFloat n => Int -> TurtleState n Source #

Tree 1

tree2 :: RealFloat n => Int -> TurtleState n Source #

Tree 2

tree3 :: RealFloat n => Int -> TurtleState n Source #

Tree 3

tree4 :: RealFloat n => Int -> TurtleState n Source #

Tree 4

tree5 :: RealFloat n => Int -> TurtleState n Source #

Tree 5

tree6 :: RealFloat n => Int -> TurtleState n Source #

Tree 6

Re-exports from Diagrams.TwoD.Path.Turtle

data TurtleState n Source #

Core turtle data type. A turtle needs to keep track of its current position, like its position, heading etc., and all the paths that it has traversed so far.

We need to record a new path, everytime an attribute like style, pen position etc changes, so that we can separately track styles for each portion of the eventual path that the turtle took.

getTurtlePath :: (Floating n, Ord n) => TurtleState n -> Path V2 n Source #

Creates a path from a turtle, ignoring the styles.

getTurtleDiagram :: (Renderable (Path V2 n) b, TypeableFloat n) => TurtleState n -> QDiagram b V2 n Any Source #

Creates a diagram from a turtle

Applies the styles to each trails in paths separately and combines them into a single diagram