Lorenz system

References

• line

• paraview_color_maps

• plot

import k3d
import numpy as np
from k3d.colormaps import paraview_color_maps

def lorenz(x, y, z, s=10, r=28, b=8/3):
    x_dot = s * (y - x)
    y_dot = r * x - y - x * z
    z_dot = x * y - b * z
    return x_dot, y_dot, z_dot

dt = 0.005
step_cnt = 10000

xs = np.empty((step_cnt + 1), dtype=np.float32)
ys = np.empty((step_cnt + 1), dtype=np.float32)
zs = np.empty((step_cnt + 1), dtype=np.float32)

xs[0], ys[0], zs[0] = (0, 1, 1.05)

for i in range(step_cnt):
    x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i])

    xs[i + 1] = xs[i] + (x_dot * dt)
    ys[i + 1] = ys[i] + (y_dot * dt)
    zs[i + 1] = zs[i] + (z_dot * dt)

plt_line = k3d.line(np.vstack([xs, ys, zs]).T,
                    width=0.05,
                    attribute=xs,
                    color_map=paraview_color_maps.Hue_L60)

plot = k3d.plot(background_color=0x1e1e1e,
                label_color=0xf0f0f0,
                grid_visible=False,
                menu_visibility=False)
plot += plt_line
plot.display()

plot.camera = [10.1646, -36.8108, -0.4144,
               -1.0736, 1.5642, 25.2671,
               0.9111, -0.0730, 0.4054]