Scripts/mandelbrot-zoom.ps1
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# Unique Concept: Deep Mandelbrot set visualization with iteration-based color cycling and escape velocity gradients. # Uses cardioid and bulb optimization for faster rendering and smooth HSV color mapping. $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 Clamp { param([double]$Value, [double]$Min, [double]$Max) if ($Value -lt $Min) { return $Min } if ($Value -gt $Max) { return $Max } return $Value } function Get-MandelbrotIteration { param( [double]$Cx, [double]$Cy, [int]$MaxIter ) # Cardioid and bulb check for main body optimization $q = ($Cx - 0.25) * ($Cx - 0.25) + $Cy * $Cy if ($q * ($q + ($Cx - 0.25)) -lt 0.25 * $Cy * $Cy) { return -1 } if (($Cx + 1) * ($Cx + 1) + $Cy * $Cy -lt 0.0625) { return -1 } $zx = 0.0 $zy = 0.0 $iter = 0 while ($iter -lt $MaxIter) { $zx2 = $zx * $zx $zy2 = $zy * $zy if ($zx2 + $zy2 -gt 4.0) { # Smooth coloring using escape velocity $smoothIter = $iter + 1 - [math]::Log([math]::Log([math]::Sqrt($zx2 + $zy2))) / [math]::Log(2) return $smoothIter } $zyTemp = 2.0 * $zx * $zy + $Cy $zx = $zx2 - $zy2 + $Cx $zy = $zyTemp $iter++ } return -1 } $width = 120 $height = 40 $maxIter = 128 # Reduced for faster rendering # Zoom into an interesting location near the Mandelbrot boundary $centerX = -0.7463 $centerY = 0.1102 $zoom = 0.005 for ($row = 0; $row -lt $height; $row++) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $x = $centerX + ($col - $width / 2.0) * $zoom / $width * 3.5 $y = $centerY + ($row - $height / 2.0) * $zoom / $height * 2.0 $iter = Get-MandelbrotIteration -Cx $x -Cy $y -MaxIter $maxIter if ($iter -lt 0) { # Inside the set - deep black with slight color variation $hue = (($col + $row) * 0.003) % 1 $rgb = Convert-HsvToRgb -Hue $hue -Saturation 0.3 -Value 0.15 $symbol = '█' } else { # Outside the set - color by iteration count $normalized = $iter / $maxIter $hue = (0.65 + $normalized * 2.5 + [math]::Sin($normalized * 6.28) * 0.1) % 1 $saturation = Clamp -Value (0.7 + 0.25 * [math]::Cos($normalized * 3.14)) -Min 0 -Max 1 $value = Clamp -Value (0.3 + 0.7 * [math]::Pow($normalized, 0.7)) -Min 0.2 -Max 1.0 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value # Symbol varies by escape speed if ($normalized -lt 0.05) { $symbol = '▓' } elseif ($normalized -lt 0.15) { $symbol = '▒' } elseif ($normalized -lt 0.3) { $symbol = '░' } elseif ($normalized -lt 0.5) { $symbol = '·' } else { $symbol = '∙' } } $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol") } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |