Scripts/nbody-gravity.ps1
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# Unique Concept: N-body gravitational simulation showing orbital mechanics and gravitational lensing effects. # Multiple masses interact via Newton's law of gravitation, creating dynamic orbital patterns. $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 = 120 $height = 40 $G = 0.5 # Gravitational constant # Initialize bodies with mass, position, velocity $bodies = @( @{ Mass = 50.0; X = 60.0; Y = 20.0; Vx = 0.0; Vy = 0.3; Hue = 0.05 }, @{ Mass = 30.0; X = 80.0; Y = 25.0; Vx = 0.0; Vy = -0.4; Hue = 0.15 }, @{ Mass = 25.0; X = 50.0; Y = 15.0; Vx = 0.35; Vy = 0.0; Hue = 0.55 }, @{ Mass = 20.0; X = 70.0; Y = 30.0; Vx = -0.3; Vy = 0.15; Hue = 0.65 }, @{ Mass = 15.0; X = 55.0; Y = 28.0; Vx = 0.2; Vy = -0.25; Hue = 0.8 } ) # Simulate orbital motion and collect trail data $trails = New-Object 'System.Collections.Generic.List[object]' $steps = 180 $dt = 0.15 for ($step = 0; $step -lt $steps; $step++) { # Calculate gravitational forces foreach ($body in $bodies) { $body.Ax = 0.0 $body.Ay = 0.0 foreach ($other in $bodies) { if ($body -eq $other) { continue } $dx = $other.X - $body.X $dy = $other.Y - $body.Y $distSq = $dx * $dx + $dy * $dy # Prevent singularities if ($distSq -lt 1.0) { $distSq = 1.0 } $dist = [math]::Sqrt($distSq) $force = $G * $other.Mass / $distSq $body.Ax += $force * ($dx / $dist) $body.Ay += $force * ($dy / $dist) } } # Update velocities and positions foreach ($body in $bodies) { $body.Vx += $body.Ax * $dt $body.Vy += $body.Ay * $dt $body.X += $body.Vx * $dt $body.Y += $body.Vy * $dt # Record trail $trails.Add([pscustomobject]@{ X = $body.X Y = $body.Y Hue = $body.Hue Age = $step }) } } # Create grid with trail intensities $grid = @{} $maxAge = $steps foreach ($point in $trails) { $gx = [int]$point.X $gy = [int]$point.Y if ($gx -ge 0 -and $gx -lt $width -and $gy -ge 0 -and $gy -lt $height) { $key = "$gx,$gy" $age = $point.Age / [double]$maxAge if ($grid.ContainsKey($key)) { $grid[$key].Count++ if ($age -gt $grid[$key].Age) { $grid[$key].Age = $age $grid[$key].Hue = $point.Hue } } else { $grid[$key] = [pscustomobject]@{ Count = 1 Age = $age Hue = $point.Hue } } } } # Render for ($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] # Color by body hue, brightness by recency and density $hue = $cell.Hue $saturation = Clamp -Value (0.6 + 0.35 * $cell.Age) -Min 0 -Max 1 $value = Clamp -Value (0.25 + 0.7 * $cell.Age + 0.15 * ($cell.Count / 10.0)) -Min 0.2 -Max 1.0 $rgb = Convert-HsvToRgb -Hue $hue -Saturation $saturation -Value $value # Symbol by density if ($cell.Count -gt 8) { $symbol = '◉' } elseif ($cell.Count -gt 5) { $symbol = '●' } elseif ($cell.Count -gt 3) { $symbol = '◎' } elseif ($cell.Count -gt 1) { $symbol = '∙' } else { $symbol = '·' } $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 |