Petal Swirl Matrix using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

def petal_shape(k, theta):

    return np.sin(k * theta)

k_values = np.linspace(2, 7, 20)  

theta = np.linspace(0, 2 * np.pi, 400)

theta_grid, k_grid = np.meshgrid(theta, k_values)

r = petal_shape(k_grid, theta_grid)

x = r * np.cos(theta_grid)

y = r * np.sin(theta_grid)

z = k_grid  

fig = plt.figure(figsize=(6, 6))

ax = fig.add_subplot(111, projection='3d')

ax.set_facecolor('black')

surface = ax.plot_surface(x, y, z, cmap='spring', edgecolor='none', alpha=0.95)

ax.set_title("Petal Swirl Matrix", color='white', fontsize=18)

ax.axis('off')

fig.colorbar(surface, shrink=0.5, aspect=10)

ax.view_init(elev=45, azim=135)

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Importing Required Libraries

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

numpy (as np): For numerical calculations and handling arrays.

matplotlib.pyplot (as plt): For creating visual plots (2D and 3D).

Axes3D: This is necessary for 3D plotting with matplotlib.

2. Defining the Petal Shape Function

def petal_shape(k, theta):

    return np.sin(k * theta)

petal_shape(k, theta): This function generates a petal shape for the pattern, based on the frequency parameter k and angle theta. It returns the radial distance r as a function of k and theta (sinusoidal oscillation).

3. Defining Parameters and Generating Grids

k_values = np.linspace(2, 7, 20)  

theta = np.linspace(0, 2 * np.pi, 400)

theta_grid, k_grid = np.meshgrid(theta, k_values)

k_values: Creates an array of 20 values ranging from 2 to 7 for the frequency parameter k.

theta: Creates an array of 400 equally spaced values for the angle theta from 0 to 

2π.

meshgrid: Creates a 2D grid of coordinates for theta and k that will be used to evaluate the petal_shape function over all combinations.

4. Generating the Radial Distance (r)

r = petal_shape(k_grid, theta_grid)

r: Uses the petal_shape function to calculate the radial distance for each (k, theta) pair. This produces the petal-like oscillations for different values of k.

5. Converting to Cartesian Coordinates

x = r * np.cos(theta_grid)

y = r * np.sin(theta_grid)

z = k_grid  

x and y: Convert the polar coordinates (r, theta) to Cartesian coordinates.

x=rcos(θ)

y=rsin(θ)

z: Set the z coordinate to the k values, so each petal is positioned at a different height based on k.

6. Creating the 3D Plot

fig = plt.figure(figsize=(6, 6))

ax = fig.add_subplot(111, projection='3d')

fig: Creates a new figure with a size of 6x6 inches.

ax: Adds a 3D subplot to the figure for plotting the surface.

7. Setting Plot Aesthetics

ax.set_facecolor('black')

surface = ax.plot_surface(x, y, z, cmap='spring', edgecolor='none', alpha=0.95)

ax.set_facecolor('black'): Sets the background color of the plot to black.

plot_surface: Plots the surface with:

cmap='spring': A spring-like color map for surface coloring.

edgecolor='none': Removes the edges of the surface grid.

alpha=0.95: Sets the surface to be slightly transparent.

8. Adding Title and Customizing Axes

ax.set_title("Petal Swirl Matrix", color='white', fontsize=18)

ax.axis('off')

ax.set_title: Adds the title "Petal Swirl Matrix" in white color and with a font size of 18.

ax.axis('off'): Hides the axes for a cleaner look.

9. Adding a Colorbar

fig.colorbar(surface, shrink=0.5, aspect=10)

Adds a color bar to the plot to show the color mapping used for the surface, with shrink=0.5 to reduce its size and aspect=10 to adjust its aspect ratio.

10. Adjusting the View Angle

ax.view_init(elev=45, azim=135)

view_init: Sets the initial view of the plot, with:

elev=45: Elevation angle of 45° (view from above).

azim=135: Azimuthal angle of 135° (rotates the view around the z-axis).

11. Displaying the Plot

plt.show()

plt.show(): Renders and displays the final 3D plot.