Apollo & Dionysus#
History is a fractal unfolding of entropy and order, a ceaseless churn wherein civilizations & belief-systems rise on the back of extracted resources, only to collapse under the weight of their own complexity
Cosmology, Geology, Biology, Ecology, Symbiotology, Teleology
Attention
Nonself vs. Self
Identity Negotiation
Salience, Expand, Reweight, Prune, Networkxw
— Yours Truly
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import matplotlib.pyplot as plt
import numpy as np
def draw_branch(x, y, angle, depth, length, ax):
if depth == 0:
return
x_end = x + length * np.cos(angle)
y_end = y + length * np.sin(angle)
ax.plot([x, x_end], [y, y_end], 'k-', lw=2)
new_length = length * 0.7
draw_branch(x_end, y_end, angle - np.pi/6, depth - 1, new_length, ax)
draw_branch(x_end, y_end, angle + np.pi/6, depth - 1, new_length, ax)
fig, ax = plt.subplots(figsize=(6, 8))
ax.set_xticks([])
ax.set_yticks([])
ax.set_frame_on(False)
draw_branch(0, -1, np.pi/2, 10, 1, ax)
plt.show()
Fig. 13 Strange Attractor (Chaotic System). This code simulates a simple chaotic attractor using the Lorenz system.#
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from scipy.integrate import solve_ivp
import numpy as np
import matplotlib.pyplot as plt
def lorenz(t, state, sigma=10, beta=8/3, rho=28):
x, y, z = state
dxdt = sigma * (y - x)
dydt = x * (rho - z) - y
dzdt = x * y - beta * z
return [dxdt, dydt, dzdt]
t_span = (0, 50)
initial_state = [0.1, 0.0, 0.0]
t_eval = np.linspace(t_span[0], t_span[1], 10000)
sol = solve_ivp(lorenz, t_span, initial_state, t_eval=t_eval)
fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, projection="3d")
ax.plot(sol.y[0], sol.y[1], sol.y[2], lw=0.5)
ax.set_title("Lorenz Attractor (Chaotic System)")
plt.show()
Fig. 14 Fractal Structure (Self-Similarity). A visualization of the famous Mandelbrot fractal, representing infinite complexity at all scales.#
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import numpy as np
import matplotlib.pyplot as plt
def mandelbrot(c, max_iter=100):
z = c
for n in range(max_iter):
if abs(z) > 2:
return n
z = z*z + c
return max_iter
xmin, xmax, ymin, ymax = -2.0, 1.0, -1.5, 1.5
width, height = 1000, 1000
x = np.linspace(xmin, xmax, width)
y = np.linspace(ymin, ymax, height)
mandelbrot_set = np.zeros((width, height))
for i in range(width):
for j in range(height):
mandelbrot_set[i, j] = mandelbrot(complex(x[i], y[j]))
plt.figure(figsize=(8, 8))
plt.imshow(mandelbrot_set.T, extent=[xmin, xmax, ymin, ymax], cmap="inferno")
plt.title("Mandelbrot Set (Fractal Structure)")
plt.colorbar()
plt.show()
Fig. 15 Immitation. This is what distinguishes humans (really? self-similar is all fractal). We reproduce language, culture, music, behaviors, weapons of extraordinarily complex nature. A ritualization of these processes stablizes its elements and creates stability and uniformity, as well as opportunities for conflict and negotiation. These codes illustrate the key points made in Sapolsky’s discussion: the limits of reductionism, the role of chaos in biological systems, and the fundamental nature of self-similarity in complex structures.#