Scripts/rossler-ribbon.ps1
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# Unique Concept: Rössler attractor - a chaotic system creating ribbon-like patterns in 3D space. # Projects the attractor onto 2D with depth-based coloring showing the folded 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)) } $width = 100 $height = 26 # Rössler attractor parameters $a = 0.2 $b = 0.2 $c = 5.7 $dt = 0.05 $x = 0.1 $y = 0.0 $z = 0.0 $points = New-Object 'System.Collections.Generic.List[object]' $steps = 4000 for ($i = 0; $i -lt $steps; $i++) { $dx = - $y - $z $dy = $x + $a * $y $dz = $b + $z * ($x - $c) $x += $dx * $dt $y += $dy * $dt $z += $dz * $dt $points.Add(@{ X = $x; Y = $y; Z = $z; Order = $i }) } # Find bounds $minX = ($points | Measure-Object -Property X -Minimum).Minimum $maxX = ($points | Measure-Object -Property X -Maximum).Maximum $minY = ($points | Measure-Object -Property Y -Minimum).Minimum $maxY = ($points | Measure-Object -Property Y -Maximum).Maximum $minZ = ($points | Measure-Object -Property Z -Minimum).Minimum $maxZ = ($points | Measure-Object -Property Z -Maximum).Maximum $grid = @{} foreach ($pt in $points) { $nx = ($pt.X - $minX) / ($maxX - $minX) $ny = ($pt.Y - $minY) / ($maxY - $minY) $nz = ($pt.Z - $minZ) / ($maxZ - $minZ) $gx = [int]($nx * ($width - 1)) $gy = [int]($ny * ($height - 1)) if ($gx -ge 0 -and $gx -lt $width -and $gy -ge 0 -and $gy -lt $height) { $key = "$gx,$gy" $age = $pt.Order / [double]$steps if ($grid.ContainsKey($key)) { $grid[$key].Count++ if ($age -gt $grid[$key].Age) { $grid[$key].Age = $age $grid[$key].Z = $nz } } else { $grid[$key] = @{ Count = 1 Age = $age Z = $nz } } } } # Render for ($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] $hue = (0.5 + $cell.Z * 0.4 + $cell.Age * 0.1) % 1 $saturation = 0.7 $value = 0.3 + 0.6 * $cell.Age + 0.15 * ($cell.Count / 5.0) if ($value -gt 1.0) { $value = 1.0 } $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $symbol = if ($cell.Count -gt 4) { '█' } elseif ($cell.Count -gt 2) { '▓' } else { '∙' } $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 |