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If you plot a sequence of point (x1, y1), (x1, y2), ..., the points can settle into one of several patterns. For example, they can enter a repeating cycle, tend towards infinity, or look chaotic. Another option is following a strange attractor. In that case, the points clearly follow some pattern but not an obvious repeating cycle.
This example plots points given by the equations:
X' = A0 + A1 * x + A2 * x * x + A3 * x * y + A4 * y + A5 * y * y
Y' = A6 + A7 * x + A8 * x * x + A9 * x * y + A10 * y + A11 * y * y
For various values of A1, A2, ... A11.
The program uses a Timer to plot points. The following code shows the Tick event
handler that draws the curve. It plots 1,000 points at a time to improve
performance and reduce flicker. For each iteration, the routine generates the
next (X, Y) point and draws it on the Bitmap named m_Bitmap. After it has
finished its 1,000 points, it draws the Bitmap onto the picCanvas control so you
can see the result.
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Private X As Double
Private Y As Double
Private Sub tmrDrawPoint_Timer()
Dim i As Integer
Dim new_x As Double
Dim new_y As Double
Dim pix_x As Integer
Dim pix_y As Integer
For i = 1 To 100
new_x = A(0) + A(1) * X + A(2) * X * X + A(3) * X * _
Y + A(4) * Y + A(5)
* Y * Y
new_y = A(6) + A(7) * X + A(8) * X * X + A(9) * X * _
Y + A(10) * Y +
A(11) * Y * Y
X = new_x
Y = new_y
pix_x = (X - m_Wxmin) / m_Wwid * m_Wid
pix_y = m_Hgt - (Y - m_Wymin) / m_Whgt * m_Hgt - 1
If (pix_x >= 0) And (pix_x < m_Wid) And _
(pix_y >= 0) And (pix_y < m_Hgt) _
Then
picCanvas.PSet (pix_x, pix_y), vbBlue
End If
Next i
End Sub
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