Scripts/complex-lissajous.ps1
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# Unique Concept: Complex Lissajous figures with multiple frequency ratios, phase relationships, and harmonic overtones. $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 = 120 $height = 30 $time = ([DateTime]::Now.Ticks / 10000000.0) % 60 # Complex Lissajous curves with multiple harmonics $harmonics = @( @{ FreqX = 3; FreqY = 4; PhaseX = 0.0; PhaseY = 0.0; Amplitude = 12; Hue = 0.0; OffsetX = 0; OffsetY = 0 }, @{ FreqX = 5; FreqY = 6; PhaseX = 1.57; PhaseY = 0.78; Amplitude = 10; Hue = 0.2; OffsetX = 0; OffsetY = 0 }, @{ FreqX = 7; FreqY = 8; PhaseX = 0.5; PhaseY = 1.2; Amplitude = 8; Hue = 0.4; OffsetX = 0; OffsetY = 0 }, @{ FreqX = 9; FreqY = 11; PhaseX = 2.1; PhaseY = 0.3; Amplitude = 6; Hue = 0.6; OffsetX = 0; OffsetY = 0 }, @{ FreqX = 13; FreqY = 15; PhaseX = 1.8; PhaseY = 2.4; Amplitude = 4; Hue = 0.8; OffsetX = 0; OffsetY = 0 } ) $grid = @{} $maxSteps = 2000 foreach ($harmonic in $harmonics) { $steps = $maxSteps for ($i = 0; $i -lt $steps; $i++) { $t = ($i / [double]$steps) * 4 * [math]::PI + $time * 0.1 $x = $harmonic.Amplitude * [math]::Sin($harmonic.FreqX * $t + $harmonic.PhaseX) $y = $harmonic.Amplitude * [math]::Sin($harmonic.FreqY * $t + $harmonic.PhaseY) $px = [int]($x + $width / 2 + $harmonic.OffsetX) $py = [int]($y + $height / 2 + $harmonic.OffsetY) if ($px -ge 0 -and $px -lt $width -and $py -ge 0 -and $py -lt $height) { $key = "$px,$py" $progress = $i / [double]$steps if (-not $grid.ContainsKey($key)) { $grid[$key] = @{ Count = 0 Hues = @() Harmonics = @() Progress = $progress } } $grid[$key].Count++ $grid[$key].Hues += $harmonic.Hue $grid[$key].Harmonics += $harmonic } } } # Render with harmonic complexity for ($y = 0; $y -lt $height; $y++) { $sb = [System.Text.StringBuilder]::new() for ($x = 0; $x -lt $width; $x++) { $key = "$x,$y" if ($grid.ContainsKey($key)) { $cell = $grid[$key] # Complex harmonic mixing $avgHue = 0 $totalWeight = 0 foreach ($hue in $cell.Hues) { $weight = 1.0 / (1.0 + [math]::Abs($hue - 0.5)) # Prefer middle hues $avgHue += $hue * $weight $totalWeight += $weight } $avgHue /= $totalWeight $hue = ($avgHue + $cell.Progress * 0.1) % 1 $saturation = 0.6 + 0.4 * ([math]::Min($cell.Count / 5.0, 1.0)) $value = 0.4 + 0.6 * ([math]::Min($cell.Count / 3.0, 1.0)) # Add harmonic complexity visualization $complexity = $cell.Harmonics.Count if ($complexity -gt 1) { $hue = ($hue + 0.1 * $complexity) % 1 $saturation = [math]::Min(1.0, $saturation + 0.1 * $complexity) } $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value # Symbol based on harmonic density $symbols = @('·', '◦', '●', '◉', '◎', '◆', '◇', '◈') $symbolIndex = [math]::Min([int]($cell.Count / 2), 7) $symbol = $symbols[$symbolIndex] $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol") } else { $null = $sb.Append("$esc[38;2;3;3;10m ") } } Write-Host ($sb.ToString() + $reset) } Write-Host $reset |