Scripts/julia-morphing.ps1
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# Unique Concept: Julia set with morphing constant parameter creating multi-frame animation effect. # The constant C rotates in complex plane, creating a dynamic transformation of the fractal 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 Clamp { param([double]$Value, [double]$Min, [double]$Max) if ($Value -lt $Min) { return $Min } if ($Value -gt $Max) { return $Max } return $Value } function Get-JuliaValue { param( [double]$Zx, [double]$Zy, [double]$Cx, [double]$Cy, [int]$MaxIter ) $x = $Zx $y = $Zy $iter = 0 while ($iter -lt $MaxIter) { $x2 = $x * $x $y2 = $y * $y if ($x2 + $y2 -gt 4.0) { $smoothIter = $iter + 1 - [math]::Log([math]::Log([math]::Sqrt($x2 + $y2))) / [math]::Log(2) return $smoothIter } $yTemp = 2.0 * $x * $y + $Cy $x = $x2 - $y2 + $Cx $y = $yTemp $iter++ } return -1 } $width = 110 $height = 38 $maxIter = 180 $zoom = 1.6 # Animate Julia constant in a circle around origin $time = ([DateTime]::Now.Ticks / 10000000.0) % 60 $angle = $time * 0.3 $radius = 0.7885 $cx = $radius * [math]::Cos($angle) $cy = $radius * [math]::Sin($angle) for ($row = 0; $row -lt $height; $row++) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $x = ($col - $width / 2.0) / ($width / 2.0) * $zoom * 1.5 $y = ($row - $height / 2.0) / ($height / 2.0) * $zoom $value = Get-JuliaValue -Zx $x -Zy $y -Cx $cx -Cy $cy -MaxIter $maxIter if ($value -lt 0) { # Inside Julia set $dist = [math]::Sqrt($x * $x + $y * $y) $hue = ($angle / 6.28 + $dist * 0.3) % 1 $rgb = Convert-HsvToRgb -Hue $hue -Saturation 0.65 -Value 0.25 $symbol = '●' } else { # Outside - color by escape iteration $normalized = $value / $maxIter $hue = ($angle / 6.28 + $normalized * 1.8 + [math]::Sin($normalized * 12.56) * 0.15) % 1 $saturation = Clamp -Value (0.6 + 0.35 * [math]::Sin($normalized * 6.28)) -Min 0 -Max 1 $value = Clamp -Value (0.35 + 0.6 * [math]::Pow($normalized, 0.5)) -Min 0.25 -Max 1.0 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value if ($normalized -lt 0.1) { $symbol = '◉' } elseif ($normalized -lt 0.25) { $symbol = '◎' } elseif ($normalized -lt 0.45) { $symbol = '○' } elseif ($normalized -lt 0.7) { $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 |