Optically Illusory

I came across a charming little optical brain-bender a while back, and wondered what would be needed to reproduce it in Excel/VBA. Not much, as it transpired (see below). I’ve golfed the code somewhat for brevity. Dump the following in an empty VBA module and run “DrawIllusion”…

Private pi As Single
Public Sub DrawIllusion()
  Dim shp, c
  pi = WorksheetFunction.pi()
  ActiveWindow.DisplayGridlines = False
  For Each shp In ActiveSheet.Shapes: shp.Delete: Next
  NewShape 0, 0, 420, 0, vbWhite
  For c = 1 To 4: DrawACircle 200, 200, 60 + (c - 1) * 40, 15, 5, -20 + (c Mod 2) * 40: Next
End Sub

Private Sub DrawACircle(x, y, r, side, gap, rotationOffset)
  Dim numSquares, i, angle, shp
  numSquares = NumToDraw(r, side, gap)
  For i = 1 To numSquares
    angle = (i - 1) * 2 * pi / numSquares
    Set shp = NewShape(x + r * Cos(angle), y + r * Sin(angle), side, angle * 180# / pi, IIf(i Mod 2 = 1, vbBlack, vbWhite))
    shp.Rotation = shp.Rotation + rotationOffset
  Next
End Sub

Private Function NumToDraw(r, side, gap)
  NumToDraw = Int(2 * pi * r / (side + gap))
  NumToDraw = NumToDraw - NumToDraw Mod 2
End Function

Private Function NewShape(x, y, side, rot, color)
  Set NewShape = ActiveSheet.Shapes.AddShape(msoShapeRectangle, x, y, side, side)
  NewShape.Rotation = rot
  NewShape.Line.ForeColor.RGB = color
  NewShape.Line.Weight = 1
  NewShape.Fill.ForeColor.RGB = RGB(128, 128, 128)
End Function