Scripts/koch-snowflake.ps1
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# Unique Concept: Koch snowflake fractal with multiple iterations showing self-similarity. # Recursive edge replacement creates increasingly complex hexagonal crystal 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)) } function Get-KochPoint { param($P1, $P2, $Depth) if ($Depth -eq 0) { return @($P1, $P2) } $dx = $P2.X - $P1.X $dy = $P2.Y - $P1.Y # Three points dividing the line $a = @{ X = $P1.X + $dx / 3; Y = $P1.Y + $dy / 3 } $b = @{ X = $P1.X + 2 * $dx / 3; Y = $P1.Y + 2 * $dy / 3 } # Peak of triangle $px = $a.X + ($b.X - $a.X) * [math]::Cos([math]::PI / 3) - ($b.Y - $a.Y) * [math]::Sin([math]::PI / 3) $py = $a.Y + ($b.X - $a.X) * [math]::Sin([math]::PI / 3) + ($b.Y - $a.Y) * [math]::Cos([math]::PI / 3) $peak = @{ X = $px; Y = $py } # Recursively process four segments $result = @() $result += Get-KochPoint -P1 $P1 -P2 $a -Depth ($Depth - 1) $result += Get-KochPoint -P1 $a -P2 $peak -Depth ($Depth - 1) $result += Get-KochPoint -P1 $peak -P2 $b -Depth ($Depth - 1) $result += Get-KochPoint -P1 $b -P2 $P2 -Depth ($Depth - 1) return $result } $width = 100 $height = 26 # Initial triangle $size = 35 $centerX = 50 $centerY = 15 $p1 = @{ X = $centerX; Y = $centerY - $size * 0.577 } $p2 = @{ X = $centerX - $size; Y = $centerY + $size * 0.289 } $p3 = @{ X = $centerX + $size; Y = $centerY + $size * 0.289 } # Generate Koch curve for each edge $depth = 4 $edge1 = Get-KochPoint -P1 $p1 -P2 $p2 -Depth $depth $edge2 = Get-KochPoint -P1 $p2 -P2 $p3 -Depth $depth $edge3 = Get-KochPoint -P1 $p3 -P2 $p1 -Depth $depth $allPoints = $edge1 + $edge2 + $edge3 # Draw lines $grid = @{} for ($i = 0; $i -lt ($allPoints.Count - 1); $i++) { $pt1 = $allPoints[$i] $pt2 = $allPoints[$i + 1] $dx = $pt2.X - $pt1.X $dy = $pt2.Y - $pt1.Y $dist = [math]::Sqrt($dx * $dx + $dy * $dy) $steps = [int]($dist * 2) if ($steps -lt 2) { $steps = 2 } for ($s = 0; $s -le $steps; $s++) { $t = $s / [double]$steps $px = [int]($pt1.X + $dx * $t) $py = [int]($pt1.Y + $dy * $t) if ($px -ge 0 -and $px -lt $width -and $py -ge 0 -and $py -lt $height) { $key = "$px,$py" $grid[$key] = $i / [double]$allPoints.Count } } } # Render 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)) { $progress = $grid[$key] $hue = (0.55 + $progress * 0.3) % 1 $saturation = 0.75 $value = 0.9 $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 |