llllvvuu · September 12, 2024 05:24
diff --git a/plot_xy_pow_z.py b/plot_xy_pow_z.py
 import numpy as np
 import matplotlib.pyplot as plt
 from mpl_toolkits.mplot3d import Axes3D

 # Set up the figure and 3D axis
 fig = plt.figure(figsize=(16, 14))
 ax = fig.add_subplot(111, projection='3d')

 # Create the grid of x and y values
 x = np.linspace(0.01, 1, 200)  # Increased resolution
 y = np.linspace(0.01, 1, 200)
 X, Y = np.meshgrid(x, y)

 # Create the two static surfaces
 Z1 = X * Y  # f(x, y) = xy
 Z2 = X      # f(x, y) = x

 # Plot the static surfaces with subtle grid lines
 surf1 = ax.plot_surface(X, Y, Z1, alpha=0.6, color='skyblue', edgecolor='royalblue', 
                        linewidth=0.05, label='f(x,y) = xy')
 surf2 = ax.plot_surface(X, Y, Z2, alpha=0.3, color='lightgreen', edgecolor='green', 
                        linewidth=0.05, label='f(x,y) = x')

 # Create and plot the hyperbolas
 k_values = np.arange(0.1, 1.1, 0.1)
 colors = plt.cm.rainbow(np.linspace(0, 1, len(k_values)))

 for k, color in zip(k_values, colors):
    x_hyp = np.linspace(k, 1, 1000)  # x values from k to 1
    y_hyp = k / x_hyp
    z_hyp_k = np.full_like(x_hyp, k)
    z_hyp_x = x_hyp
    
    # Plot (x, k/x, k) hyperbola
    ax.plot(x_hyp, y_hyp, z_hyp_k, color=color, linewidth=3, label=f'k = {k:.1f}')
    
    # Plot (x, k/x, x) curve
    ax.plot(x_hyp, y_hyp, z_hyp_x, color=color, linewidth=2)
    
    # Add dotted mapping lines
    for i in range(0, len(x_hyp), 50):  # Adjust the step to control the number of lines
        ax.plot([x_hyp[i], x_hyp[i]], [y_hyp[i], y_hyp[i]], [z_hyp_k[i], z_hyp_x[i]], 
                color=color, linestyle=':', alpha=0.7, linewidth=1)

 # Set labels and title
 ax.set_xlabel('X', fontsize=12, labelpad=10)
 ax.set_ylabel('Y', fontsize=12, labelpad=10)
 ax.set_zlabel('Z', fontsize=12, labelpad=10)
 ax.set_title('exponentiation by U(0, 1) applied to f(x, y) = xy contourwise yields f(x, y) = x', fontsize=16)

 # Set axis limits
 ax.set_xlim(0, 1)
 ax.set_ylim(0, 1)
 ax.set_zlim(0, 1)

 # Adjust the view angle
 ax.view_init(elev=20, azim=250)

 # Add a legend
 ax.legend(loc='upper left', bbox_to_anchor=(1.1, 1), fontsize=10)

 # Adjust the layout to make room for the legend
 plt.tight_layout()

 # Show the plot
 # plt.show()

 # Uncomment the following line to save the figure as a png
 plt.savefig('3d_graph_with_hyperbolas_and_subtle_grids.png', dpi=300, bbox_inches='tight')
	import numpy as np
	import matplotlib.pyplot as plt
	from mpl_toolkits.mplot3d import Axes3D

	# Set up the figure and 3D axis
	fig = plt.figure(figsize=(16, 14))
	ax = fig.add_subplot(111, projection='3d')

	# Create the grid of x and y values
	x = np.linspace(0.01, 1, 200) # Increased resolution
	y = np.linspace(0.01, 1, 200)
	X, Y = np.meshgrid(x, y)

	# Create the two static surfaces
	Z1 = X * Y # f(x, y) = xy
	Z2 = X # f(x, y) = x

	# Plot the static surfaces with subtle grid lines
	surf1 = ax.plot_surface(X, Y, Z1, alpha=0.6, color='skyblue', edgecolor='royalblue',
	linewidth=0.05, label='f(x,y) = xy')
	surf2 = ax.plot_surface(X, Y, Z2, alpha=0.3, color='lightgreen', edgecolor='green',
	linewidth=0.05, label='f(x,y) = x')

	# Create and plot the hyperbolas
	k_values = np.arange(0.1, 1.1, 0.1)
	colors = plt.cm.rainbow(np.linspace(0, 1, len(k_values)))

	for k, color in zip(k_values, colors):
	x_hyp = np.linspace(k, 1, 1000) # x values from k to 1
	y_hyp = k / x_hyp
	z_hyp_k = np.full_like(x_hyp, k)
	z_hyp_x = x_hyp

	# Plot (x, k/x, k) hyperbola
	ax.plot(x_hyp, y_hyp, z_hyp_k, color=color, linewidth=3, label=f'k = {k:.1f}')

	# Plot (x, k/x, x) curve
	ax.plot(x_hyp, y_hyp, z_hyp_x, color=color, linewidth=2)

	# Add dotted mapping lines
	for i in range(0, len(x_hyp), 50): # Adjust the step to control the number of lines
	ax.plot([x_hyp[i], x_hyp[i]], [y_hyp[i], y_hyp[i]], [z_hyp_k[i], z_hyp_x[i]],
	color=color, linestyle=':', alpha=0.7, linewidth=1)

	# Set labels and title
	ax.set_xlabel('X', fontsize=12, labelpad=10)
	ax.set_ylabel('Y', fontsize=12, labelpad=10)
	ax.set_zlabel('Z', fontsize=12, labelpad=10)
	ax.set_title('exponentiation by U(0, 1) applied to f(x, y) = xy contourwise yields f(x, y) = x', fontsize=16)

	# Set axis limits
	ax.set_xlim(0, 1)
	ax.set_ylim(0, 1)
	ax.set_zlim(0, 1)

	# Adjust the view angle
	ax.view_init(elev=20, azim=250)

	# Add a legend
	ax.legend(loc='upper left', bbox_to_anchor=(1.1, 1), fontsize=10)

	# Adjust the layout to make room for the legend
	plt.tight_layout()

	# Show the plot
	# plt.show()

	# Uncomment the following line to save the figure as a png
	plt.savefig('3d_graph_with_hyperbolas_and_subtle_grids.png', dpi=300, bbox_inches='tight')