NexToken

NexToken#

Nodes, edges, scale#

Scroll to bottom: anticipated the Schwab-Brin talking points

                     1. Phonetics
                                 \
                2. Temperament -> 4. Modes/Phonetics -> 5. NexToken/Temperament -> 6. Emotion/Scale
                                 /
                                 3. Scales
../_images/blanche.png

These six topics cover all aspects of music. Can you imagine that in 10 years we have implants in our brains (This is before Elon’s Neuralink)? We can instantly get feedback on the emotional impact of information in realtime on the masses?#

Hide code cell source 
import networkx as nx
import matplotlib.pyplot as plt
import numpy as np

# Create a directed graph
G = nx.DiGraph()

# Add nodes representing different levels (subatomic, atomic, cosmic, financial, social)
levels = ['i: Obama', 'ii7♭5: Trump', 'V7: Clinton']

# Add nodes to the graph
G.add_nodes_from(levels)

# Add edges to represent the flow of information (photons)
# Assuming the flow is directional from more fundamental levels to more complex ones
edges = [('ii7♭5: Trump', 'V7: Clinton'),
         ('V7: Clinton', 'i: Obama'),]

# Add edges to the graph
G.add_edges_from(edges)

# Define positions for the nodes in a circular layout
pos = nx.circular_layout(G)

# Set the figure size (width, height)
plt.figure(figsize=(10, 10))  # Adjust the size as needed

# Draw the main nodes
nx.draw_networkx_nodes(G, pos, node_color='lightblue', node_size=30000)

# Draw the edges with arrows and create space between the arrowhead and the node
nx.draw_networkx_edges(G, pos, arrowstyle='->', arrowsize=20, edge_color='grey',
                       connectionstyle='arc3,rad=0.2')  # Adjust rad for more/less space

# Add smaller red nodes (photon nodes) exactly on the circular layout
for edge in edges:
    # Calculate the vector between the two nodes
    vector = pos[edge[1]] - pos[edge[0]]
    # Calculate the midpoint
    mid_point = pos[edge[0]] + 0.5 * vector
    # Normalize to ensure it's on the circle
    radius = np.linalg.norm(pos[edge[0]])
    mid_point_on_circle = mid_point / np.linalg.norm(mid_point) * radius
    # Draw the small red photon node at the midpoint on the circular layout
    plt.scatter(mid_point_on_circle[0], mid_point_on_circle[1], c='lightpink', s=500, zorder=3)

    # Draw a small lime green arrow inside the red node to indicate direction
    arrow_vector = vector / np.linalg.norm(vector) * 0.1  # Scale down arrow size
    plt.arrow(mid_point_on_circle[0] - 0.05 * arrow_vector[0],
              mid_point_on_circle[1] - 0.05 * arrow_vector[1],
              arrow_vector[0], arrow_vector[1],
              head_width=0.03, head_length=0.05, fc='limegreen', ec='limegreen', zorder=4)

# Draw the labels for the main nodes
nx.draw_networkx_labels(G, pos, font_size=18, font_weight='normal')

# Add a legend for "Photon/Info"
plt.scatter([], [], c='lightpink', s=100, label='Chord Progression')  # Empty scatter for the legend
plt.legend(scatterpoints=1, frameon=True, labelspacing=1, loc='upper right')

# Set the title and display the plot
plt.title('Emotional Arc', fontsize=15)
plt.axis('off')
plt.show()
../_images/0bfc31f264c449d6410a06144fc6b48d8b8994e4e2e591aedc08dd3a9b99f813.png
../_images/blanche.png

Faith, Love, Hope. Trump, Clinton, Obama. Clinton is technology V7. Obama is resentment i. No, no, no. Yes, yes. And Trump is entitlement ii7b5. Basically, Trump is the past, undergoing decline, reminiscing about the past, the golden past, la belle époque. Obama is painting the vision for the future for the sufferers, hope, just like Jesus. Clinton is like Silicon Valley, the now, you know, the technology and engineering, the numbers, the data, empiricism. Your characterization of these political figures as symbols of broader societal forces is intriguing, though I think it might be worth exploring their roles with a bit more nuance. Clinton, as a symbol of technology, represents the optimism of the 1990s—a time when globalization and the internet were seen as harbingers of progress. His presidency coincided with the rise of Silicon Valley, and his policies often reflected a technocratic approach to governance, emphasizing data, pragmatism, and economic expansion. However, this technocratic focus also sowed the seeds for future discontent, as the benefits of technological and economic growth weren’t evenly distributed. Obama, framed as resentment, is perhaps more accurately seen as the embodiment of aspiration and the promise of progress, particularly for those who felt left behind or marginalized by the rapid changes of the previous decades. His message of hope resonated with many who were disillusioned by the status quo, offering a vision of an inclusive future. However, this very vision also exposed deep divides in American society, as it highlighted ongoing inequalities and the unfulfilled promises of the American Dream. Trump, symbolizing entitlement and the past, certainly reflects a yearning for a bygone era—“Make America Great Again” is the essence of nostalgia for a time when many felt more secure in their social and economic status. His appeal to a return to a “golden age” speaks to a segment of society that perceives itself as losing ground in the face of globalization, technological advancement, and shifting cultural norms. The entitlement comes from a belief that something has been unfairly taken away and must be restored. These figures represent distinct visions of America’s trajectory: Clinton with a data-driven, technocratic present; Obama with a hopeful but contentious vision of a more equitable future; and Trump with a backward-looking, protectionist past. Each embodies a particular response to the rapid changes and challenges of our time, with their own set of contradictions and complexities.#

                    1. Nodes
                            \
                2. Edges -> 4. Nodes -> 5. Edges -> 6. Scale
                            /
                            3. Scale

ii \(\mu\) Single Note#

  • ii \(f(t)\) Phonetics: 39 40 Fractals \(440Hz \times 2^{\frac{N}{12}}\), \(S_0(t) \times e^{logHR}\), \(\frac{S N(d_1)}{K N(d_2)} \times e^{rT}\)

Hide code cell source 
import numpy as np
import matplotlib.pyplot as plt

# Parameters
sample_rate = 44100  # Hz
duration = 20.0       # seconds
A4_freq = 440.0      # Hz

# Time array
t = np.linspace(0, duration, int(sample_rate * duration), endpoint=False)

# Fundamental frequency (A4)
signal = np.sin(2 * np.pi * A4_freq * t)

# Adding overtones (harmonics)
harmonics = [2, 3, 4, 5, 6, 7, 8, 9]  # First few harmonics
amplitudes = [0.5, 0.25, 0.15, 0.1, 0.05, 0.03, 0.01, 0.005]  # Amplitudes for each harmonic

for i, harmonic in enumerate(harmonics):
    signal += amplitudes[i] * np.sin(2 * np.pi * A4_freq * harmonic * t)

# Perform FFT (Fast Fourier Transform)
N = len(signal)
yf = np.fft.fft(signal)
xf = np.fft.fftfreq(N, 1 / sample_rate)

# Modify the x-axis to represent a timeline from biblical times to today
timeline_labels = ['2000 BC', '1000 BC', 'Birth of Jesus', 'St. Paul', 'Middle Ages', 'Renaissance', 'Modern Era']
timeline_positions = np.linspace(0, 2024, len(timeline_labels))  # positions corresponding to labels

# Down-sample the y-axis data to match the length of timeline_positions
yf_sampled = 2.0 / N * np.abs(yf[:N // 2])
yf_downsampled = np.interp(timeline_positions, np.linspace(0, 2024, len(yf_sampled)), yf_sampled)

# Plot the frequency spectrum with modified x-axis
plt.figure(figsize=(12, 6))
plt.plot(timeline_positions, yf_downsampled, color='navy', lw=1.5)

# Aesthetics improvements
plt.title('Simulated Frequency Spectrum with Historical Timeline', fontsize=16, weight='bold')
plt.xlabel('Historical Timeline', fontsize=14)
plt.ylabel('Reverence', fontsize=14)
plt.xticks(timeline_positions, labels=timeline_labels, fontsize=12)
plt.ylim(0, None)

# Shading the period from Birth of Jesus to St. Paul
plt.axvspan(timeline_positions[2], timeline_positions[3], color='lightpink', alpha=0.5)

# Annotate the shaded region
plt.annotate('Birth of Jesus to St. Paul',
             xy=(timeline_positions[2], 0.7), xycoords='data',
             xytext=(timeline_positions[3] + 200, 0.5), textcoords='data',
             arrowprops=dict(facecolor='black', arrowstyle="->"),
             fontsize=12, color='black')

# Remove top and right spines
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)

# Customize ticks
plt.xticks(timeline_positions, labels=timeline_labels, fontsize=12)
plt.yticks(fontsize=12)

# Light grid
plt.grid(color='grey', linestyle=':', linewidth=0.5)

# Show the plot
plt.tight_layout()


plt.show()
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../_images/c6a091816fb8a7f77550b5b2f45074d961485aff114516b4970f3bebf2be1bc8.png

  • V7 \(S(t)\) Temperament: \(440Hz \times 2^{\frac{N}{12}}\)

  • i \(h(t)\) Scales: 12 unique notes x 7 modes (Bach covers only x 2 modes in WTK)

    • Soulja Boy has an incomplete Phrygian in PBS

    • Flamenco Phyrgian scale is equivalent to a Mixolydian V9♭♯9♭13

V7 \(\sigma\) Chord Stacks#

  • \((X'X)^T \cdot X'Y\): Mode: \( \mathcal{F}(t) = \alpha \cdot \left( \prod_{i=1}^{n} \frac{\partial \psi_i(t)}{\partial t} \right) + \beta \cdot \int_{0}^{t} \left( \sum_{j=1}^{m} \frac{\partial \phi_j(\tau)}{\partial \tau} \right) d\tau\)

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import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 7
tick_labels = [
    "Root-iADL (i)",
    "Hunter-gather (ii7♭5)", "Peasant (III)", "Farmer (iv)", "Manufacturer (V7♭9♯9♭13)",
    "Energy (VI)", "Transport (VII)"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()
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../_images/27e040d08e633f630e1f9c273497a6101713684d3a59bc65c4f9ab4012e1af26.png

i \(\%\) Predict NexToken#

  • \(\alpha, \beta, t\) NexToken: Attention, to the minor, major, dom7, and half-dim7 groupings, is all you need 41

Hide code cell source 
import matplotlib.pyplot as plt
import numpy as np

# Clock settings; f(t) random disturbances making "paradise lost"
clock_face_radius = 1.0
number_of_ticks = 9
tick_labels = [
    "Sun-Genomics", "Chlorophyll-Transcriptomics", "Flora-Proteomics", "Animals-Metabolomics",
    "Wood-Epigenomics", "Coal-Lipidomics", "Hydrocarbons-Glycomics", "Renewable-Metagenomics", "Nuclear-Phenomics"
]

# Calculate the angles for each tick (in radians)
angles = np.linspace(0, 2 * np.pi, number_of_ticks, endpoint=False)
# Inverting the order to make it counterclockwise
angles = angles[::-1]

# Create figure and axis
fig, ax = plt.subplots(figsize=(8, 8))
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_aspect('equal')

# Draw the clock face
clock_face = plt.Circle((0, 0), clock_face_radius, color='lightgrey', fill=True)
ax.add_patch(clock_face)

# Draw the ticks and labels
for angle, label in zip(angles, tick_labels):
    x = clock_face_radius * np.cos(angle)
    y = clock_face_radius * np.sin(angle)
    
    # Draw the tick
    ax.plot([0, x], [0, y], color='black')
    
    # Positioning the labels slightly outside the clock face
    label_x = 1.1 * clock_face_radius * np.cos(angle)
    label_y = 1.1 * clock_face_radius * np.sin(angle)
    
    # Adjusting label alignment based on its position
    ha = 'center'
    va = 'center'
    if np.cos(angle) > 0:
        ha = 'left'
    elif np.cos(angle) < 0:
        ha = 'right'
    if np.sin(angle) > 0:
        va = 'bottom'
    elif np.sin(angle) < 0:
        va = 'top'
    
    ax.text(label_x, label_y, label, horizontalalignment=ha, verticalalignment=va, fontsize=10)

# Remove axes
ax.axis('off')

# Show the plot
plt.show()
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../_images/70de0a53a875dc3a54a3423648462f09ab630e23443cd31eaedf80639499556c.png

  • \(SV_t'\) Emotion: How many degrees of freedom does a composer, performer, or audience member have within a genre? We’ve roped in the audience as a reminder that music has no passive participants

Hide code cell source 
import numpy as np
import matplotlib.pyplot as plt

# Define the total utility function U(Q)
def total_utility(Q):
    return 100 * np.log(Q + 1)  # Logarithmic utility function for illustration

# Define the marginal utility function MU(Q)
def marginal_utility(Q):
    return 100 / (Q + 1)  # Derivative of the total utility function

# Generate data
Q = np.linspace(1, 100, 500)  # Quantity range from 1 to 100
U = total_utility(Q)
MU = marginal_utility(Q)

# Plotting
plt.figure(figsize=(14, 7))

# Plot Total Utility
plt.subplot(1, 2, 1)
plt.plot(Q, U, label=r'Total Utility $U(Q) = 100 \log(Q + 1)$', color='blue')
plt.title('Total Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Total Utility (U)')
plt.legend()
plt.grid(True)

# Plot Marginal Utility
plt.subplot(1, 2, 2)
plt.plot(Q, MU, label=r'Marginal Utility $MU(Q) = \frac{dU(Q)}{dQ} = \frac{100}{Q + 1}$', color='red')
plt.title('Marginal Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Marginal Utility (MU)')
plt.legend()
plt.grid(True)

# Adding some calculus notation and Greek symbols
plt.figtext(0.5, 0.02, r"$MU(Q) = \frac{dU(Q)}{dQ} = \lim_{\Delta Q \to 0} \frac{U(Q + \Delta Q) - U(Q)}{\Delta Q}$", ha="center", fontsize=12)

plt.tight_layout()
plt.show()
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../_images/afa91f0bcf337e9d0a0901707fe1aa1c7a332b551fb5b7af920037b2996fc9ee.png
Hide code cell source 
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.cm import ScalarMappable
from matplotlib.colors import LinearSegmentedColormap, PowerNorm

def gaussian(x, mean, std_dev, amplitude=1):
    return amplitude * np.exp(-0.9 * ((x - mean) / std_dev) ** 2)

def overlay_gaussian_on_line(ax, start, end, std_dev):
    x_line = np.linspace(start[0], end[0], 100)
    y_line = np.linspace(start[1], end[1], 100)
    mean = np.mean(x_line)
    y = gaussian(x_line, mean, std_dev, amplitude=std_dev)
    ax.plot(x_line + y / np.sqrt(2), y_line + y / np.sqrt(2), color='red', linewidth=2.5)

fig, ax = plt.subplots(figsize=(10, 10))

intervals = np.linspace(0, 100, 11)
custom_means = np.linspace(1, 23, 10)
custom_stds = np.linspace(.5, 10, 10)

# Change to 'viridis' colormap to get gradations like the older plot
cmap = plt.get_cmap('viridis')
norm = plt.Normalize(custom_stds.min(), custom_stds.max())
sm = ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])

median_points = []

for i in range(10):
    xi, xf = intervals[i], intervals[i+1]
    x_center, y_center = (xi + xf) / 2 - 20, 100 - (xi + xf) / 2 - 20
    x_curve = np.linspace(custom_means[i] - 3 * custom_stds[i], custom_means[i] + 3 * custom_stds[i], 200)
    y_curve = gaussian(x_curve, custom_means[i], custom_stds[i], amplitude=15)
    
    x_gauss = x_center + x_curve / np.sqrt(2)
    y_gauss = y_center + y_curve / np.sqrt(2) + x_curve / np.sqrt(2)
    
    ax.plot(x_gauss, y_gauss, color=cmap(norm(custom_stds[i])), linewidth=2.5)
    median_points.append((x_center + custom_means[i] / np.sqrt(2), y_center + custom_means[i] / np.sqrt(2)))

median_points = np.array(median_points)
ax.plot(median_points[:, 0], median_points[:, 1], '--', color='grey')
start_point = median_points[0, :]
end_point = median_points[-1, :]
overlay_gaussian_on_line(ax, start_point, end_point, 24)

ax.grid(True, linestyle='--', linewidth=0.5, color='grey')
ax.set_xlim(-30, 111)
ax.set_ylim(-20, 87)

# Create a new ScalarMappable with a reversed colormap just for the colorbar
cmap_reversed = plt.get_cmap('viridis').reversed()
sm_reversed = ScalarMappable(cmap=cmap_reversed, norm=norm)
sm_reversed.set_array([])

# Existing code for creating the colorbar
cbar = fig.colorbar(sm_reversed, ax=ax, shrink=1, aspect=90)

# Specify the tick positions you want to set
custom_tick_positions = [0.5, 5, 8, 10]  # example positions, you can change these
cbar.set_ticks(custom_tick_positions)

# Specify custom labels for those tick positions
custom_tick_labels = ['5', '3', '1', '0']  # example labels, you can change these
cbar.set_ticklabels(custom_tick_labels)

# Label for the colorbar
cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)


# Label for the colorbar
cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)


cbar.set_label(r'♭', rotation=0, labelpad=15, fontstyle='italic', fontsize=24)

# Add X and Y axis labels with custom font styles
ax.set_xlabel(r'Principal Component', fontstyle='italic')
ax.set_ylabel(r'Emotional State', rotation=0, fontstyle='italic', labelpad=15)

# Add musical modes as X-axis tick labels
# musical_modes = ["Ionian", "Dorian", "Phrygian", "Lydian", "Mixolydian", "Aeolian", "Locrian"]
greek_letters = ['α', 'β','γ', 'δ', 'ε', 'ζ', 'η'] # 'θ' , 'ι', 'κ'
mode_positions = np.linspace(ax.get_xlim()[0], ax.get_xlim()[1], len(greek_letters))
ax.set_xticks(mode_positions)
ax.set_xticklabels(greek_letters, rotation=0)

# Add moods as Y-axis tick labels
moods = ["flow", "control", "relaxed", "bored", "apathy","worry", "anxiety", "arousal"]
mood_positions = np.linspace(ax.get_ylim()[0], ax.get_ylim()[1], len(moods))
ax.set_yticks(mood_positions)
ax.set_yticklabels(moods)

# ... (rest of the code unchanged)


plt.tight_layout()
plt.show()
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../_images/8c315e442439684d434a857660fcf4b8647e72c4d941d87b4ffe36e7294e04d9.png
../_images/blanche.png

Emotion & Affect as Outcomes & Freewill. And the predictors \(\beta\) are MQ-TEA: Modes (ionian, dorian, phrygian, lydian, mixolydian, locrian), Qualities (major, minor, dominant, suspended, diminished, half-dimished, augmented), Tensions (7th), Extensions (9th, 11th, 13th), and Alterations (♯, ♭) 42#

                    1. f(t)
                           \
               2. S(t) ->  4. Nxb:t(X'X).X'Y -> 5. b -> 6. df
                           /
                           3. h(t)

moiety

Hide code cell source 
import pandas as pd

# Data for the table
data = {
    "Thinker": [
        "Heraclitus", "Plato", "Aristotle", "Augustine", "Thomas Aquinas", 
        "Machiavelli", "Descartes", "Spinoza", "Leibniz", "Hume", 
        "Kant", "Hegel", "Nietzsche", "Marx", "Freud", 
        "Jung", "Schumpeter", "Foucault", "Derrida", "Deleuze"
    ],
    "Epoch": [
        "Ancient", "Ancient", "Ancient", "Late Antiquity", "Medieval",
        "Renaissance", "Early Modern", "Early Modern", "Early Modern", "Enlightenment",
        "Enlightenment", "19th Century", "19th Century", "19th Century", "Late 19th Century",
        "Early 20th Century", "Early 20th Century", "Late 20th Century", "Late 20th Century", "Late 20th Century"
    ],
    "Lineage": [
        "Implicit", "Socratic lineage", "Builds on Plato",
        "Christian synthesis", "Christianizes Aristotle", 
        "Acknowledges predecessors", "Breaks tradition", "Synthesis of traditions", "Cartesian", "Empiricist roots",
        "Hume influence", "Dialectic evolution", "Heraclitus influence",
        "Hegelian critique", "Original psychoanalysis",
        "Freudian divergence", "Marxist roots", "Nietzsche, Marx",
        "Deconstruction", "Nietzsche, Spinoza" 
    ]
}

# Create DataFrame
df = pd.DataFrame(data)

# Display DataFrame
print(df)
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           Thinker               Epoch                    Lineage
0       Heraclitus             Ancient                   Implicit
1            Plato             Ancient           Socratic lineage
2        Aristotle             Ancient            Builds on Plato
3        Augustine      Late Antiquity        Christian synthesis
4   Thomas Aquinas            Medieval    Christianizes Aristotle
5      Machiavelli         Renaissance  Acknowledges predecessors
6        Descartes        Early Modern           Breaks tradition
7          Spinoza        Early Modern    Synthesis of traditions
8          Leibniz        Early Modern                  Cartesian
9             Hume       Enlightenment           Empiricist roots
10            Kant       Enlightenment             Hume influence
11           Hegel        19th Century        Dialectic evolution
12       Nietzsche        19th Century       Heraclitus influence
13            Marx        19th Century          Hegelian critique
14           Freud   Late 19th Century    Original psychoanalysis
15            Jung  Early 20th Century        Freudian divergence
16      Schumpeter  Early 20th Century              Marxist roots
17        Foucault   Late 20th Century            Nietzsche, Marx
18         Derrida   Late 20th Century             Deconstruction
19         Deleuze   Late 20th Century         Nietzsche, Spinoza
Hide code cell source 
import networkx as nx
import matplotlib.pyplot as plt

def add_family_edges(G, parent, depth, names, scale=1):
    if depth == 0 or not names:
        return parent
    
    # Adding children based on depth and given names
    children = names.pop(0)
    for child in children:
        G.add_edge(parent, child)
        
        # Recursive call to add descendants of the current child, but avoid adding children for certain nodes
        if child not in ["GPT", "AGI", "Transformer", "Google Brain"]:  # Nodes that should not have children
            add_family_edges(G, child, depth - 1, names, scale * 0.9)

def create_extended_fractal_tree():
    G = nx.Graph()
    
    # Start with the initial node 'God'
    root = "God"
    G.add_node(root)
    
    # Add 'Adam' as a child of 'God'
    adam = "Adam"
    G.add_edge(root, adam)
    
    # Correct list of descendants
    descendants = [
        ["Seth", "Cain"],             # Children of Adam
        ["Enos", "Noam"],             # Children of Seth; 'Noam' represents a less significant line
        ["Abraham", "Others"],        # Dashed line for skipped generations from Enos to Abraham
        ["Isaac", "Ishmael"],         # Children of Abraham
        ["Jacob", "Esau"],            # Children of Isaac
        ["Judah", "Levi"],            # Children of Jacob
        ["Ilya Sutskever", "Sergey Brin"], # Modern "children" from Judah as missing links
        ["OpenAI", "AlexNet"],        # Children of Ilya Sutskever
        ["GPT", "AGI"],               # Children of OpenAI, should not have children themselves
        # ["Google Brain", "Transformer"], # Children of Sergey Brin, should not have children themselves
        ["Elon Musk/Cyborg"],         # Elon Musk as a conceptual descendant
        ["Tesla", "SpaceX", "Boring Company", "Neuralink", "X", "xAI"] # Elon Musk's companies as children of Elon Musk
    ]
    
    # Generate edges recursively
    add_family_edges(G, adam, len(descendants), descendants)
    
    # Manually add dashed edges to indicate "missing links"
    missing_link_edges = [
        ("Enos", "Abraham"),              # Dashed line for skipped generations
        ("Judah", "Ilya Sutskever"),
        ("Judah", "Sergey Brin"),
        ("AlexNet", "Elon Musk/Cyborg"),  # Dashed line indicating conceptual link from AlexNet
        ("Google Brain", "Elon Musk/Cyborg") # Dashed line indicating conceptual link from Google Brain
    ]

    # Add missing link edges to the graph
    G.add_edges_from([("Enos", "Abraham"), ("Judah", "Ilya Sutskever"), ("Judah", "Sergey Brin"), ("AlexNet", "Elon Musk/Cyborg")])

    # Adding Sergey Brin's children correctly
    G.add_edge("Sergey Brin", "Google Brain")
    G.add_edge("Sergey Brin", "Transformer")

    return G, missing_link_edges

def visualize_tree(seed=42):
    # Generate the extended fractal tree with Musk and Brin's additions
    extended_tree_graph, missing_link_edges = create_extended_fractal_tree()

    # Visualization
    plt.figure(figsize=(12, 10))
    pos = nx.spring_layout(extended_tree_graph, seed=seed)  # Add seed for random layout

    # Define color maps for nodes
    color_map = []
    for node in extended_tree_graph.nodes():
        if node == "God":
            color_map.append("lightblue")  # Color for God
        elif node in ["OpenAI", "AlexNet", "GPT", "AGI", "Google Brain", "Transformer"]:
            color_map.append("lightgreen")  # Color for AI entities
        elif node == "Elon Musk/Cyborg" or node in ["Tesla", "SpaceX", "Boring Company", "Neuralink", "X", "xAI"]:
            color_map.append("yellow")  # Color for Elon Musk and his companies
        else:
            color_map.append("lightpink")  # Color for human figures

    # Draw all solid edges first
    solid_edges = [edge for edge in extended_tree_graph.edges() if edge not in missing_link_edges]
    nx.draw(extended_tree_graph, pos, edgelist=solid_edges, with_labels=True, node_size=1000, node_color=color_map, font_size=10, font_weight="bold", edge_color="grey", width=2)

    # Draw the missing link edges as dashed lines
    nx.draw_networkx_edges(
        extended_tree_graph,
        pos,
        edgelist=missing_link_edges,
        style="dashed",
        edge_color="lightgray",  
        width=2
    )

    plt.axis('off')
    plt.show()

# Visualize with a specific seed
visualize_tree(seed=6)
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../_images/ae800a37c168467ee5bd79a2d36db7a2297c100350cedc2990434a4a0c7e9aa7.png
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