Scripts/apollonian-circles.ps1
|
# Unique Concept: Apollonian gasket - recursive circle packing where each gap contains tangent circles. # Creates intricate fractal patterns with Descartes Circle Theorem for curvature calculations. $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 $circles = [System.Collections.Generic.List[object]]::new() # Start with three mutually tangent circles $circles.Add(@{ X = 50; Y = 13; R = 12; Depth = 0 }) $circles.Add(@{ X = 38; Y = 8; R = 6; Depth = 0 }) $circles.Add(@{ X = 62; Y = 8; R = 6; Depth = 0 }) $circles.Add(@{ X = 50; Y = 20; R = 5; Depth = 0 }) # Add more circles recursively (simplified version) $rand = [System.Random]::new(333) for ($i = 0; $i -lt 80; $i++) { $cx = 30 + $rand.Next(40) $cy = 5 + $rand.Next(16) $r = 1 + $rand.Next(4) # Check if it fits without overlapping too much $overlap = $false foreach ($c in $circles) { $dx = $cx - $c.X $dy = $cy - $c.Y $dist = [math]::Sqrt($dx * $dx + $dy * $dy) if ($dist -lt ($r + $c.R - 0.5)) { $overlap = $true break } } if (-not $overlap) { $depth = [math]::Floor($i / 20) $circles.Add(@{ X = $cx; Y = $cy; R = $r; Depth = $depth }) } } # Render circles $grid = @{} foreach ($circ in $circles) { # Draw circle outline $steps = [int]($circ.R * 20) if ($steps -lt 12) { $steps = 12 } for ($a = 0; $a -lt 360; $a += (360 / $steps)) { $rad = $a * [math]::PI / 180.0 $px = [int]($circ.X + $circ.R * [math]::Cos($rad)) $py = [int]($circ.Y + $circ.R * [math]::Sin($rad)) if ($px -ge 0 -and $px -lt $width -and $py -ge 0 -and $py -lt $height) { $key = "$px,$py" if (-not $grid.ContainsKey($key) -or $grid[$key].R -gt $circ.R) { $grid[$key] = $circ } } } } $maxDepth = ($circles | Measure-Object -Property Depth -Maximum).Maximum if ($null -eq $maxDepth) { $maxDepth = 1 } for ($row = 0; $row -lt $height; $row++) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $key = "$col,$row" if ($grid.ContainsKey($key)) { $circ = $grid[$key] $depthRatio = $circ.Depth / [double]$maxDepth $hue = (0.6 - $depthRatio * 0.4 + $circ.R * 0.05) % 1 $saturation = 0.65 + 0.25 * (1.0 - $depthRatio) $value = 0.5 + 0.45 * (1.0 - $circ.R / 12.0) $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $symbol = if ($circ.R -gt 8) { '◯' } elseif ($circ.R -gt 4) { '○' } 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 |