X(n) = Sin(A * Y(n - 1)) - Z(n - 1) * Cos(B * X(n - 1))
    Y(n) = Z(n) * Sin(C * X(n - 1)) - Cos(D * Y(n - 1))
    Z(n) = Sin(X(n - 1))

The example plots the X-Y, Y-Z, or X-Z coordinates of the points visited.

Instead of coloring each point visited in red, green, or blue, this example increases the point's red, green, or blue color components. This means points visited many times become brighter. It also allows colors to combine. You can plot the attractor's X-Y, Y-Z, and X-Z components on the same picture in different colors and combinations of red, green, and blue will show where the plots overlap.

' Draw the curve.
Private Sub DrawCurve()
    Const XMIN As Double = -2.1
    Const XMAX As Double = 2.1
    Const YMIN As Double = -2.1
    Const YMAX As Double = 2.1
    Const ZMIN As Double = -1.2
    Const ZMAX As Double = 1.2

    Dim xoff As Double
    Dim yoff As Double
    Dim zoff As Double
    Dim xscale As Double
    Dim yscale As Double
    Dim zscale As Double
    Dim x As Double
    Dim y As Double
    Dim z As Double
    Dim x2 As Double
    Dim y2 As Double
    Dim i As Integer

    ' Get the drawing parameters.
    GetParameters()
    picCanvas.ForeColor = PointColor

    Select Case SelectedPlane
        Case PlaneTypes.plane_XY
            xoff = m_Wid / 2
            yoff = m_Hgt / 2
            xscale = m_Wid / (XMAX - XMIN)
            yscale = m_Hgt / (YMAX - YMIN)
        Case PlaneTypes.plane_XZ
            xoff = m_Wid / 2
            zoff = m_Hgt / 2
            xscale = m_Wid / (XMAX - XMIN)
            zscale = m_Hgt / (ZMAX - ZMIN)
        Case PlaneTypes.plane_YZ
            yoff = m_Wid / 2
            zoff = m_Hgt / 2
            yscale = m_Wid / (YMAX - YMIN)
            zscale = m_Hgt / (ZMAX - ZMIN)
    End Select

    ' Compute the values.
    x = X0
    y = Y0
    z = Z0
    i = 0

    Dim dr As Integer
    Dim dg As Integer
    Dim db As Integer
    If PointColor.R > 0 Then dr = 16
    If PointColor.G > 0 Then dg = 16
    If PointColor.B > 0 Then db = 16

    Do While Running
        ' Move to the next point.
        x2 = Sin(A * y) - z * Cos(B * x)
        y2 = z * Sin(C * x) - Cos(D * y)
        z = Sin(x)
        x = x2
        y = y2

        ' Plot the point.
        If True Then
            Dim ix As Integer
            Dim iy As Integer
            Select Case SelectedPlane
                Case PlaneTypes.plane_XY
                    ix = CInt(x * xscale + xoff)
                    iy = CInt(y * yscale + yoff)
                Case PlaneTypes.plane_XZ
                    ix = CInt(x * xscale + xoff)
                    iy = CInt(z * zscale + zoff)
                Case PlaneTypes.plane_YZ
                    ix = CInt(y * yscale + yoff)
                    iy = CInt(z * zscale + zoff)
            End Select

            Dim clr As Color = m_Bm.GetPixel(ix, iy)

            Dim new_r As Integer = clr.R + dr
            If new_r > 255 Then new_r = 255
            Dim new_g As Integer = clr.G + dg
            If new_g > 255 Then new_g = 255
            Dim new_b As Integer = clr.B + db
            If new_b > 255 Then new_b = 255

            clr = Color.FromArgb(255, new_r, new_g, new_b)
            m_Bm.SetPixel(ix, iy, clr)
        Else
            Select Case SelectedPlane
                Case PlaneTypes.plane_XY
                    m_Bm.SetPixel(CInt(x * xscale + xoff), _
                        CInt(y * yscale + yoff), PointColor)
                Case PlaneTypes.plane_XZ
                    m_Bm.SetPixel(CInt(x * xscale + xoff), _
                        CInt(z * zscale + zoff), PointColor)
                Case PlaneTypes.plane_YZ
                    m_Bm.SetPixel(CInt(y * yscale + yoff), _
                        CInt(z * zscale + zoff), PointColor)
            End Select
        End If

        ' To make things faster, only DoEvents
        ' every 100 times.
        i = i + 1
        If i > 100 Then
            i = 0
            picCanvas.Refresh()
            Application.DoEvents()
        End If
    Loop
End Sub