commit a59288a4d06d9d77319bf9becd1ddee057c60596
parent 5d4bb7661a0fd16a49cfc3a79ff6148766beab96
Author: Kris Yotam <75515498+krisyotam@users.noreply.github.com>
Date: Fri, 11 Oct 2024 20:05:11 -0500
Create reinman.py
Diffstat:
| A | progs.py/reinman.py | | | 106 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
1 file changed, 106 insertions(+), 0 deletions(-)
diff --git a/progs.py/reinman.py b/progs.py/reinman.py
@@ -0,0 +1,106 @@
+##########################################
+# Name: Kris Yotam #
+# Program: Reinman #
+# Date: 10/11/2024 #
+# Description: This program visualizes #
+# the Riemann surface for the square #
+# root function and allows dynamic #
+# interaction, multiple surfaces, #
+# critical points analysis, and a basic #
+# GUI interface. #
+##########################################
+
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib.widgets import Slider
+import tkinter as tk
+
+# Create a mesh grid for complex numbers (z = x + iy)
+theta = np.linspace(0, 2 * np.pi, 100)
+r = np.linspace(0.01, 2, 50) # Start from 0.01 to avoid singularity at 0
+theta, r = np.meshgrid(theta, r)
+x = r * np.cos(theta)
+y = r * np.sin(theta)
+
+# Define the function to plot the surface
+def plot_surface(exponent):
+ # Compute the square root of complex numbers z = x + iy
+ z = x + 1j * y
+ w = z ** exponent
+
+ # Real and imaginary parts of the surface
+ X1 = np.real(w)
+ Y1 = np.imag(w)
+ Z1 = np.log(r) # Using log(r) to make visualization more informative
+
+ ax.clear() # Clear previous plots
+ # Color map based on height (Z1)
+ cmap = plt.get_cmap('coolwarm') # Blue to light blue gradient
+
+ # Plot the first branch of the square root with the updated color scheme
+ ax.plot_surface(x, y, X1, rstride=1, cstride=1,
+ facecolors=cmap((Z1 - Z1.min()) / (Z1.max() - Z1.min())),
+ alpha=0.9, edgecolor='k')
+
+ # Plot the second branch (negative square root)
+ ax.plot_surface(x, y, -X1, rstride=1, cstride=1,
+ facecolors=cmap((Z1 - Z1.min()) / (Z1.max() - Z1.min())),
+ alpha=0.9, edgecolor='k')
+
+ # Labels and title
+ ax.set_xlabel('Re(z)')
+ ax.set_ylabel('Im(z)')
+ ax.set_zlabel('Re(z^n)')
+ ax.set_title(f'Riemann Surface for z^{exponent} with Custom Colors')
+ plt.draw()
+
+# Function to calculate critical points
+def critical_points(exponent):
+ # Calculate critical points based on the derivative
+ # For z^n, critical points occur at z=0 for n > 1
+ if exponent > 1:
+ return [0] # Critical point at origin
+ return []
+
+# Create sliders for interactive control
+fig, ax = plt.subplots(figsize=(10, 8), subplot_kw={'projection': '3d'})
+plt.subplots_adjust(left=0.1, bottom=0.25)
+
+# Create slider for exponent
+ax_exponent = plt.axes([0.1, 0.1, 0.65, 0.03]) # [left, bottom, width, height]
+slider_exponent = Slider(ax_exponent, 'Exponent', 1, 5, valinit=2)
+
+# Update function for slider
+def update(val):
+ plot_surface(slider_exponent.val)
+ cp = critical_points(slider_exponent.val)
+ print("Critical Points:", cp)
+
+slider_exponent.on_changed(update)
+plot_surface(slider_exponent.val)
+
+# Basic GUI setup using tkinter
+def create_gui():
+ root = tk.Tk()
+ root.title("Riemann Surface Visualizer")
+
+ label = tk.Label(root, text="Welcome to the Riemann Surface Visualizer!")
+ label.pack()
+
+ instruction = tk.Label(root, text="Use the slider to change the exponent.")
+ instruction.pack()
+
+ # Add a button to close the GUI
+ close_button = tk.Button(root, text="Close", command=root.quit)
+ close_button.pack()
+
+ root.mainloop()
+
+# Show GUI in a separate thread
+import threading
+
+gui_thread = threading.Thread(target=create_gui)
+gui_thread.start()
+
+plt.show() # Show the plot
