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kushalkolar merged 2 commits into from
Sep 1, 2024
Merged

add lorenz attractor example #595

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add lorenz example
clewis7 Aug 26, 2024
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clewis7 Sep 1, 2024
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92 changes: 92 additions & 0 deletions examples/desktop/misc/lorenz_animation.py
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"""
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"
)

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=8, colors=graphic.colors[0])
scatter_markers.append(marker)

# initialize time
time = 0


def animate(supblot):
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 = 75

# 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.run()