Turtle

0.1

Types/Turtle/LSystem.ps1

<#
.SYNOPSIS
    Draws a L-system pattern.
.DESCRIPTION
    Generates a pattern using a L-system.

    The initial string (Axiom) is transformed according to the rules provided for a specified number of iterations.
.LINK
    https://en.wikipedia.org/wiki/L-system
.EXAMPLE
    # Box Fractal L-System
    $Box = 'F-F-F-F'
    $Fractal = 'F-F+F+F-F'
    
    $turtle.Clear().LSystem(
            $Box,
            [Ordered]@{ F = $Fractal },
            3,
            @{
                F = { $this.Forward(10) }
                J = { $this.Jump(10) }
                '\+' = { $this.Rotate(90) }
                '-' = { $this.Rotate(-90) }
            }
    ).Pattern.Save("$pwd/BoxFractalLSystem.svg")
.EXAMPLE
    # Fractal L-System
    $Box = 'FFFF-FFFF-FFFF-FFFF'
    $Fractal = 'F-F+F+F-F'
        
    $turtle.Clear().LSystem(
            $Box,
            [Ordered]@{ F = $Fractal },
            4,
            @{
                F = { $this.Forward(10) }
                J = { $this.Jump(10) }
                '\+' = { $this.Rotate(90) }
                '-' = { $this.Rotate(-90) }
            }
    ).Symbol.Save("$pwd/FractalLSystem.svg")
.EXAMPLE
    # Arrowhead Fractal L-System
    $Box = 'FF-FF-FF'
    $Fractal = 'F-F+F+F-F'
    
    
    $turtle.Clear().LSystem(
            $Box,
            [Ordered]@{ F = $Fractal },
            4,
            @{
                F = { $this.Forward(10) }
                J = { $this.Jump(10) }
                '\+' = { $this.Rotate(90) }
                '-' = { $this.Rotate(-90) }
            }
    ).Pattern.Save("$pwd/ArrowheadFractalLSystem.svg")
.EXAMPLE
    # Tetroid LSystem
    $turtle.Clear().LSystem(
            'F',
            [Ordered]@{ F = 'F+F+F+F' +
                '+JJJJ+' +
                'F+F+F+F' +
                '++JJJJ' +
                'F+F+F+F' +
                '++JJJJ' +
                'F+F+F+F' +
                '++JJJJ' +
                '-JJJJ'
            },
            3,
            @{
                F = { $this.Forward(10) }
                J = { $this.Jump(10) }
                '\+' = { $this.Rotate(90) }
                '-' = { $this.Rotate(-90) }
            }
    ).Pattern.Save("$pwd/TetroidLSystem.svg")

.EXAMPLE
    $turtle.Clear().LSystem(
        'F',
        [Ordered]@{ F = '
F+F+F+F +JJJJ+ F+F+F+F ++ JJJJ' },
        3,
        @{
            F = { $this.Forward(10) }
            J = { $this.Jump(10) }
            '\+' = { $this.Rotate(90) }
            '-' = { $this.Rotate(-90) }
        }
    ).Pattern.Save("$pwd/LSystemCool1.svg")
.EXAMPLE
    Move-Turtle LSystem F-F-F-F ([Ordered]@{F='F-F+F+F-F'}) 3 (
        [Ordered]@{
            F = { $this.Forward(10) }
            J = { $this.Jump(10) }
            '\+' = { $this.Rotate(90) }
            '-' = { $this.Rotate(-90) }
        }
    )
    
#>
param(
[Alias('Start', 'StartString', 'Initiator')]
[string]
$Axiom,

[Alias('Rules', 'ProductionRules')]
[Collections.IDictionary]
$Rule = [Ordered]@{},

[Alias('Iterations', 'Steps', 'IterationCount','StepCount')]
[int]
$N = 2,

[Collections.IDictionary]
$Variable = @{}
)

if ($n -lt 1) { return $Axiom}

$currentState = "$Axiom"
$combinedPattern = "(?>$($Rule.Keys -join '|'))"    
foreach ($iteration in 1..$n) {
    $currentState = $currentState -replace $combinedPattern, {
        $match = $_
        $matchingRule = $rule["$match"]
        if ($matchingRule -is [ScriptBlock]) {                        
            return "$(& $matchingRule $match)"
        } else {
            return $matchingRule
        }
    }    
}

$localReplacement = [Ordered]@{}
foreach ($key in $variable.Keys) {
    $localReplacement[$key] = 
        if ($variable[$key] -is [ScriptBlock]) {
            [ScriptBlock]::Create($variable[$key])
        } else {
            $variable[$key]
        }
}

$finalState = $currentState
$null = foreach ($character in $finalState.ToCharArray()) {
    foreach ($key in $Variable.Keys) {
        if ($character -match $key) {
            $action = $localReplacement[$key]
            if ($action -is [ScriptBlock]) {
                . $action $character
            } else {
                $action
            } 
        }
    }
}
return $this