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# Lorenz

VTKEx/Python/Visualization/Lorenz

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### Code

Lorenz.py

    #!/usr/bin/env python

    """
    Create an iso-surface of the Lorenz attractor.

    Here we visualize a Lorenz strange attractor by integrating the Lorenz equations in a volume.
    The number of visits in each voxel is recorded as a scalar function.
    The surface is extracted via marching cubes using a visit value of 50.
    The number of integration steps is 10 million, in a volume of dimensions 200 x 200 x 200.
    The surface roughness is caused by the discrete nature of the evaluation function.

    """
    import vtk

    def main():
        colors = vtk.vtkNamedColors()

        Pr = 10.0  # The Lorenz parameters
        b = 2.667
        r = 28.0
        # x = 0.0
        # y = 0.0
        # z = 0.0  # starting (and current) x, y, z
        h = 0.01  # integration step size
        resolution = 200  # slice resolution
        iterations = 10000000  # number of iterations
        xmin = -30.0  # x, y, z range for voxels
        xmax = 30.0
        ymin = -30.0
        ymax = 30.0
        zmin = -10.0
        zmax = 60.0

        # Take a stab at an integration step size.
        xIncr = resolution / (xmax - xmin)
        yIncr = resolution / (ymax - ymin)
        zIncr = resolution / (zmax - zmin)

        print("The Lorenz Attractor\n")
        print(" Pr =", Pr)
        print(" b =", b)
        print(" r =", r)
        print(" integration step size =", h)
        print(" slice resolution =", resolution)
        print(" # of iterations =", iter)
        print(" specified range:")
        print("     x: {:f}, {:f}".format(xmin, xmax))
        print("     y: {:f}, {:f}".format(ymin, ymax))
        print("     z: {:f}, {:f}".format(zmin, zmax))

        x = vtk.vtkMath.Random(xmin, xmax)
        y = vtk.vtkMath.Random(ymin, ymax)
        z = vtk.vtkMath.Random(zmin, zmax)
        print(" starting at {:f}, {:f}, {:f}".format(x, y, z))
        # allocate memory for the slices
        sliceSize = resolution * resolution
        numPts = sliceSize * resolution
        scalars = vtk.vtkShortArray()
        for i in range(0, numPts):
            scalars.InsertTuple1(i, 0)
        for j in range(0, iterations):
            # Integrate to the next time step.
            xx = x + h * Pr * (y - x)
            yy = y + h * (x * (r - z) - y)
            zz = z + h * (x * y - (b * z))

            x = xx
            y = yy
            z = zz

            # Calculate the voxel index.
            if xmax > x > xmin and ymax > y > ymin and zmax > z > zmin:
                xxx = int(float(xx - xmin) * xIncr)
                yyy = int(float(yy - ymin) * yIncr)
                zzz = int(float(zz - zmin) * zIncr)
                index = xxx + yyy * resolution + zzz * sliceSize
                scalars.SetTuple1(index, scalars.GetTuple1(index) + 1)

        volume = vtk.vtkStructuredPoints()
        volume.GetPointData().SetScalars(scalars)
        volume.SetDimensions(resolution, resolution, resolution)
        volume.SetOrigin(xmin, ymin, zmin)
        volume.SetSpacing((xmax - xmin) / resolution, (ymax - ymin) / resolution, (zmax - zmin) / resolution)

        print(" contouring...")
        # Do the graphics dance.
        renderer = vtk.vtkRenderer()
        renWin = vtk.vtkRenderWindow()
        renWin.AddRenderer(renderer)

        iren = vtk.vtkRenderWindowInteractor()
        iren.SetRenderWindow(renWin)

        # Create iso-surface
        contour = vtk.vtkContourFilter()
        contour.SetInputData(volume)
        contour.SetValue(0, 50)

        # Create mapper.
        mapper = vtk.vtkPolyDataMapper()
        mapper.SetInputConnection(contour.GetOutputPort())
        mapper.ScalarVisibilityOff()

        # Create actor.
        actor = vtk.vtkActor()
        actor.SetMapper(mapper)
        actor.GetProperty().SetColor(colors.GetColor3d("PaleTurquoise"))

        renderer.AddActor(actor)
        renderer.SetBackground(colors.GetColor3d("PeachPuff"))

        renWin.SetSize(640, 480)

        # interact with data
        renWin.Render()

        iren.Start()

    if __name__ == '__main__':
        main()