Scripts/pythagorean-tree.ps1
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# Unique Concept: Pythagorean tree fractal - squares branching at right angles creating organic growth. # Each square spawns two smaller squares rotated 45° creating a tree-like structure. $ErrorActionPreference = 'Stop' $esc = [char]27 $reset = "$esc[0m" function Convert-HsvToRgb { param([double]$Hue, [double]$Saturation, [double]$Value) $h = ($Hue % 1) * 6 $sector = [math]::Floor($h) $fraction = $h - $sector $p = $Value * (1 - $Saturation) $q = $Value * (1 - $fraction * $Saturation) $t = $Value * (1 - (1 - $fraction) * $Saturation) switch ($sector) { 0 { $r = $Value; $g = $t; $b = $p } 1 { $r = $q; $g = $Value; $b = $p } 2 { $r = $p; $g = $Value; $b = $t } 3 { $r = $p; $g = $q; $b = $Value } 4 { $r = $t; $g = $p; $b = $Value } default { $r = $Value; $g = $p; $b = $q } } return @([int][math]::Round($r * 255), [int][math]::Round($g * 255), [int][math]::Round($b * 255)) } $width = 100 $height = 26 $grid = @{} function Add-PythagoreanSquare { param($CenterX, $CenterY, $Size, $Angle, $Depth, $MaxDepth) if ($Depth -gt $MaxDepth -or $Size -lt 0.6) { return } # Draw filled square $halfSize = $Size / 2.0 for ($dy = - $halfSize; $dy -le $halfSize; $dy += 0.5) { for ($dx = - $halfSize; $dx -le $halfSize; $dx += 0.5) { # Rotate point $rotX = $dx * [math]::Cos($Angle) - $dy * [math]::Sin($Angle) $rotY = $dx * [math]::Sin($Angle) + $dy * [math]::Cos($Angle) $px = [int]($CenterX + $rotX) $py = [int]($CenterY + $rotY) if ($px -ge 0 -and $px -lt $script:width -and $py -ge 0 -and $py -lt $script:height) { $key = "$px,$py" if (-not $script:grid.ContainsKey($key) -or $script:grid[$key].Size -gt $Size) { $script:grid[$key] = @{ Size = $Size Depth = $Depth } } } } } # Calculate branch positions $topCenterX = $CenterX + $halfSize * [math]::Sin($Angle) $topCenterY = $CenterY - $halfSize * [math]::Cos($Angle) $newSize = $Size * 0.7 $angleLeft = $Angle - [math]::PI / 4 $angleRight = $Angle + [math]::PI / 4 $offsetDist = $newSize / 2.0 + $halfSize / 2.0 $leftX = $topCenterX + $offsetDist * [math]::Sin($angleLeft) $leftY = $topCenterY - $offsetDist * [math]::Cos($angleLeft) $rightX = $topCenterX + $offsetDist * [math]::Sin($angleRight) $rightY = $topCenterY - $offsetDist * [math]::Cos($angleRight) Add-PythagoreanSquare -CenterX $leftX -CenterY $leftY -Size $newSize -Angle $angleLeft -Depth ($Depth + 1) -MaxDepth $MaxDepth Add-PythagoreanSquare -CenterX $rightX -CenterY $rightY -Size $newSize -Angle $angleRight -Depth ($Depth + 1) -MaxDepth $MaxDepth } # Start with base square Add-PythagoreanSquare -CenterX 50 -CenterY 24 -Size 8 -Angle 0 -Depth 0 -MaxDepth 7 # Render $maxDepth = ($grid.Values | Measure-Object -Property Depth -Maximum).Maximum if ($null -eq $maxDepth) { $maxDepth = 1 } for ($row = 0; $row -lt $height; $row++) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $key = "$col,$row" if ($grid.ContainsKey($key)) { $cell = $grid[$key] $depthRatio = $cell.Depth / [double]$maxDepth $hue = (0.15 + $depthRatio * 0.3) % 1 $saturation = 0.7 $value = 0.9 - 0.5 * $depthRatio $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $symbol = '█' $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol") } else { $null = $sb.Append("$esc[38;2;8;8;12m ") } } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |