"""

Lorenz System Animation

=======================

Example of the Lorenz attractor.

"""

# test_example = false

# sphinx_gallery_pygfx_docs = 'animate 10s'

import fastplotlib as fpl

import numpy as np

# generate data

def lorenz(xyz, *, s=10, r=28, b=2.667):

"""

Parameters

----------

xyz : array-like, shape (3,)

Point of interest in three-dimensional space.

s, r, b : float

Parameters defining the Lorenz attractor.

Returns

-------

xyz_dot : array, shape (3,)

Values of the Lorenz attractor's partial derivatives at *xyz*.

"""

x, y, z = xyz

x_dot = s * (y - x)

y_dot = r * x - y - x * z

z_dot = x * y - b * z

return np.array([x_dot, y_dot, z_dot])

dt = 0.01

num_steps = 3_000

lorenz_data = np.empty((5, num_steps + 1, 3))

for i in range(5):

xyzs = np.empty((num_steps + 1, 3)) # Need one more for the initial values

xyzs[0] = (0., (i * 0.3) + 1, 1.05) # Set initial values

# Step through "time", calculating the partial derivatives at the current point

# and using them to estimate the next point

for j in range(num_steps):

xyzs[j + 1] = xyzs[j] + lorenz(xyzs[j]) * dt

lorenz_data[i] = xyzs

figure = fpl.Figure(

cameras="3d",

controller_types="fly",

size=(700, 560)

)

lorenz_line = figure[0, 0].add_line_collection(data=lorenz_data, thickness=.1, cmap="tab10")

scatter_markers = list()

for graphic in lorenz_line:

marker = figure[0, 0].add_scatter(graphic.data.value[0], sizes=16, colors=graphic.colors[0])

scatter_markers.append(marker)

# initialize time

time = 0

def animate(subplot):

global time

time += 2

if time >= xyzs.shape[0]:

time = 0

for scatter, g in zip(scatter_markers, lorenz_line):

scatter.data = g.data.value[time]

figure[0, 0].add_animations(animate)

figure.show()

# set initial camera position to make animation in gallery render better

figure[0, 0].camera.world.z = 80

# NOTE: `if __name__ == "__main__"` is NOT how to use fastplotlib interactively

# please see our docs for using fastplotlib interactively in ipython and jupyter

if __name__ == "__main__":

print(__doc__)

fpl.loop.run()