Scripts/hilbert-spectrum.ps1
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# Unique Concept: Order-5 Hilbert curve traced with corner-aware box drawing and spectral progression along the path. $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 $Value } function Get-HilbertPoint { param( [int]$Index, [int]$Order ) $x = 0 $y = 0 $t = $Index $n = 1 -shl $Order for ($s = 1; $s -lt $n; $s = $s * 2) { $rx = ($t -band 2) -shr 1 $ry = (($t -band 1) -bxor $rx) if ($ry -eq 0) { if ($rx -eq 1) { $x = $s - 1 - $x $y = $s - 1 - $y } $swap = $x $x = $y $y = $swap } $x += $rx * $s $y += $ry * $s $t = $t -shr 2 } return [pscustomobject]@{ X = $x; Y = $y } } $order = 5 $size = 1 -shl $order $total = $size * $size $xs = New-Object 'int[]' $total $ys = New-Object 'int[]' $total for ($i = 0; $i -lt $total; $i++) { $pt = Get-HilbertPoint -Index $i -Order $order $xs[$i] = $pt.X $ys[$i] = $pt.Y } $grid = @{} for ($i = 0; $i -lt $total; $i++) { $x = $xs[$i] $y = $ys[$i] if (-not $grid.ContainsKey("$x,$y")) { $prevX = if ($i -gt 0) { $x - $xs[$i - 1] } else { 0 } $prevY = if ($i -gt 0) { $y - $ys[$i - 1] } else { 0 } $nextX = if ($i -lt $total - 1) { $xs[$i + 1] - $x } else { 0 } $nextY = if ($i -lt $total - 1) { $ys[$i + 1] - $y } else { 0 } $grid["$x,$y"] = [pscustomobject]@{ Index = $i PrevX = $prevX PrevY = $prevY NextX = $nextX NextY = $nextY } } } $cornerMap = @{ '-1,0|0,1' = '┛' '-1,0|0,-1' = '┓' '1,0|0,1' = '┗' '1,0|0,-1' = '┏' '0,1|1,0' = '┏' '0,1|-1,0' = '┓' '0,-1|1,0' = '┗' '0,-1|-1,0' = '┛' } for ($row = $size - 1; $row -ge 0; $row--) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $size; $col++) { $key = "$col,$row" if ($grid.ContainsKey($key)) { $cell = $grid[$key] $progress = $cell.Index / [double]($total - 1) $entryX = - $cell.PrevX $entryY = - $cell.PrevY $exitX = $cell.NextX $exitY = $cell.NextY if ($entryX -eq 0 -and $entryY -eq 0) { $symbol = '●' } elseif ($exitX -eq 0 -and $exitY -eq 0) { $symbol = '◎' } elseif ($entryY -eq 0 -and $exitY -eq 0) { $symbol = '━' } elseif ($entryX -eq 0 -and $exitX -eq 0) { $symbol = '┃' } else { $lookup = "$entryX,$entryY|$exitX,$exitY" if ($cornerMap.ContainsKey($lookup)) { $symbol = $cornerMap[$lookup] } else { $symbol = '╳' } } $hue = ($progress + 0.18 * [math]::Sin(($col + $row) * 0.28) + 0.12 * [math]::Cos(($col - $row) * 0.31)) % 1 if ($hue -lt 0) { $hue += 1 } $saturation = Clamp -Value (0.5 + 0.42 * [math]::Sin($progress * [math]::PI)) -Min 0 -Max 1 $value = Clamp -Value (0.28 + 0.7 * [math]::Pow($progress, 0.6)) -Min 0.25 -Max 1 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $token = "$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol" $null = $sb.Append($token) $null = $sb.Append($token) } else { $null = $sb.Append("$esc[38;2;8;9;12m ") } } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |