Scripts/chromatic-lorenz.ps1
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# Unique Concept: Lorenz attractor plotted across a terminal grid with time-coded hues and speed-weighted highlights. $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 = 96 $height = 40 $steps = 5200 $dt = 0.008 $sigma = 10.0 $rho = 28.0 $beta = 8.0 / 3.0 $x = 0.1 $y = 0.0 $z = 0.0 $points = New-Object 'System.Collections.Generic.List[object]' $minX = [double]::PositiveInfinity $maxX = [double]::NegativeInfinity $minZ = [double]::PositiveInfinity $maxZ = [double]::NegativeInfinity $minSpeed = [double]::PositiveInfinity $maxSpeed = [double]::NegativeInfinity for ($i = 0; $i -lt $steps; $i++) { $dx = $sigma * ($y - $x) $dy = $x * ($rho - $z) - $y $dz = ($x * $y) - ($beta * $z) $speed = [math]::Sqrt($dx * $dx + $dy * $dy + $dz * $dz) $x += $dx * $dt $y += $dy * $dt $z += $dz * $dt if ($x -lt $minX) { $minX = $x } if ($x -gt $maxX) { $maxX = $x } if ($z -lt $minZ) { $minZ = $z } if ($z -gt $maxZ) { $maxZ = $z } if ($speed -lt $minSpeed) { $minSpeed = $speed } if ($speed -gt $maxSpeed) { $maxSpeed = $speed } $null = $points.Add([pscustomobject]@{ X = $x Y = $y Z = $z Index = $i Speed = $speed }) } if ($maxX -eq $minX) { $maxX = $minX + 1e-6 } if ($maxZ -eq $minZ) { $maxZ = $minZ + 1e-6 } if ($maxSpeed -eq $minSpeed) { $maxSpeed = $minSpeed + 1e-6 } $grid = @{} foreach ($p in $points) { $gx = [math]::Floor((($p.X - $minX) / ($maxX - $minX)) * ($width - 1)) $gy = [math]::Floor((($p.Z - $minZ) / ($maxZ - $minZ)) * ($height - 1)) if ($gx -lt 0) { $gx = 0 } if ($gx -ge $width) { $gx = $width - 1 } if ($gy -lt 0) { $gy = 0 } if ($gy -ge $height) { $gy = $height - 1 } $key = "$gx,$gy" $progress = $p.Index / ($steps - 1) $speedFactor = ($p.Speed - $minSpeed) / ($maxSpeed - $minSpeed) if (-not $grid.ContainsKey($key) -or $p.Index -gt $grid[$key].Index) { $char = if ($speedFactor -gt 0.75) { '✶' } elseif ($speedFactor -gt 0.35) { '•' } else { '·' } $grid[$key] = [pscustomobject]@{ Index = $p.Index Hue = $progress Saturation = 0.9 Value = 0.35 + (0.6 * $speedFactor) Char = $char } } } for ($row = $height - 1; $row -ge 0; $row--) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $key = "$col,$row" if ($grid.ContainsKey($key)) { $cell = $grid[$key] $rgb = Convert-HsvToRgb -Hue $cell.Hue -Saturation $cell.Saturation -Value $cell.Value $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$($cell.Char)") } else { $null = $sb.Append("$esc[38;2;12;12;18m ") } } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |