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[markov_chain_I] Hamilton's chain animation #457

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Jun 17, 2024
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[markov_chain_I] Hamilton's chain animation #457

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32 changes: 23 additions & 9 deletions lectures/markov_chains_I.md
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Original file line number Diff line number Diff line change
Expand Up @@ -58,6 +58,9 @@ import numpy as np
import networkx as nx
from matplotlib import cm
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from IPython.display import HTML
```

## Definitions and examples
Expand Down Expand Up @@ -812,16 +815,27 @@ Now we plot the sequence
fig = plt.figure()
ax = fig.add_subplot(projection='3d')

ψ_t = iterate_ψ(ψ_0, P, 20)

ax.scatter(ψ_t[:,0], ψ_t[:,1], ψ_t[:,2], c='r', s=60)
ax.view_init(30, 210)

mc = qe.MarkovChain(P)
ψ_star = mc.stationary_distributions[0]
ax.scatter(ψ_star[0], ψ_star[1], ψ_star[2], c='k', s=60)
def update(n):
ψ_t = iterate_ψ(ψ_0, P, n+1)

ax.clear()
ax.set_xlim([0, 1])
ax.set_ylim([0, 1])
ax.set_zlim([0, 1])
ax.view_init(30, 210)

for i, point in enumerate(ψ_t):
ax.scatter(point[0], point[1], point[2], color='r', s=60, alpha=(i+1)/len(ψ_t))

mc = qe.MarkovChain(P)
ψ_star = mc.stationary_distributions[0]
ax.scatter(ψ_star[0], ψ_star[1], ψ_star[2], c='k', s=60)

return fig,

plt.show()
anim = FuncAnimation(fig, update, frames=range(20), blit=False, repeat=False)
plt.close()
HTML(anim.to_jshtml())
```

Here
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