Scripts/hyperbolic-bloom.ps1
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# Unique Concept: Poincaré-disk bloom using hyperbolic reflections and geodesic interference bands. $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 } $width = 96 $height = 36 $segments = 7 $segmentAngle = (2 * [math]::PI) / $segments for ($row = $height - 1; $row -ge 0; $row--) { $sb = [System.Text.StringBuilder]::new() for ($col = 0; $col -lt $width; $col++) { $nx = ($col / [double]($width - 1)) * 2.0 - 1.0 $ny = ($row / [double]($height - 1)) * 2.0 - 1.0 $rSquared = ($nx * $nx) + ($ny * $ny) if ($rSquared -ge 1.0) { $null = $sb.Append("$esc[38;2;8;9;12m ") continue } $r = [math]::Sqrt($rSquared) $theta = [math]::Atan2($ny, $nx) if ($theta -lt 0) { $theta += 2 * [math]::PI } $segmentIndex = [math]::Floor($theta / $segmentAngle) $thetaLocal = $theta - ($segmentIndex * $segmentAngle) if ($thetaLocal -gt ($segmentAngle / 2)) { $thetaLocal = $segmentAngle - $thetaLocal } $thetaNormalized = $thetaLocal / ($segmentAngle / 2) $hyperRadius = 2.0 * [math]::Atanh($r) $geodesic = [math]::Sin($hyperRadius * 2.35 + $thetaNormalized * [math]::PI * 3.6) $hue = (($segmentIndex / [double]$segments) + 0.12 * $thetaNormalized + 0.1 * [math]::Sin($hyperRadius * 1.17)) % 1 if ($hue -lt 0) { $hue += 1 } $saturation = Clamp -Value (0.58 + 0.35 * [math]::Exp(-$hyperRadius * 0.35)) -Min 0 -Max 1 $value = Clamp -Value (0.2 + 0.78 * [math]::Exp( - ($hyperRadius - 1.1) * ($hyperRadius - 1.1) * 0.45) + 0.1 * [math]::Sin($thetaNormalized * [math]::PI)) -Min 0.18 -Max 1.0 $symbol = if ([math]::Abs($geodesic) -lt 0.18) { '✦' } elseif ($geodesic -gt 0.45) { '◉' } elseif ($geodesic -lt -0.45) { '◇' } else { '·' } $edgeGlow = Clamp -Value (0.6 - ($r * 0.45)) -Min 0 -Max 1 $value = Clamp -Value ($value + (0.25 * $edgeGlow)) -Min 0.2 -Max 1.0 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value $null = $sb.Append("$esc[38;2;$($rgb[0]);$($rgb[1]);$($rgb[2])m$symbol") } Write-Host ($sb.ToString() + $reset) } |