Coral Torus Bloom Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

u=np.linspace(0,2*np.pi,100)

v=np.linspace(0,2*np.pi,100)

u,v=np.meshgrid(u,v)

R=1

r=0.3

bloom=0.1*np.sin(5*u)*np.cos(7*v)

x=(R+r*np.cos(v)+bloom)*np.cos(u)

y=(R+r*np.cos(v)+bloom)*np.sin(u)

z=r*np.sin(v)+bloom

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='plasma', edgecolor='none', alpha=0.95)

ax.set_xlim([-1.5,1.5])

ax.set_ylim([-1.5,1.5])

ax.set_zlim([-1.5,1.5])

ax.axis('off')

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

plt.title('Coral Torus Bloom',color='white',fontsize=18)

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): Used for numerical operations and array manipulations.

matplotlib.pyplot (as plt): Used for plotting 2D/3D graphics.

Axes3D: Enables 3D plotting in matplotlib.

2. Creating Meshgrid Parameters

u = np.linspace(0, 2 * np.pi, 100)

v = np.linspace(0, 2 * np.pi, 100)

u, v = np.meshgrid(u, v)

u and v: Arrays of 100 values evenly spaced from 0 to 

2π, representing angles.

meshgrid: Creates 2D coordinate grids from u and v for parameterizing a surface.

3. Defining Torus Parameters and Surface Perturbation

R = 1     

r = 0.3   

bloom = 0.1 * np.sin(5 * u) * np.cos(7 * v)

R: Major radius (distance from center of tube to center of torus).

r: Minor radius (radius of the tube).

bloom: A sinusoidal perturbation to add organic "bloom" effects to the torus surface, like coral growth.

4. Parametric Equations of the Deformed Torus

x = (R + r * np.cos(v) + bloom) * np.cos(u)

y = (R + r * np.cos(v) + bloom) * np.sin(u)

z = r * np.sin(v) + bloom

These are the parametric equations of a torus modified by the bloom effect:

x=(R+rcos(v)+bloom)cos(u)

y=(R+rcos(v)+bloom)sin(u)

z=rsin(v)+bloom

5. Creating the 3D Plot

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

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

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

ax: Adds a 3D subplot to the figure.

6. Plot Settings and Aesthetics

ax.set_facecolor('black')

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

ax.set_facecolor: Sets the background of the 3D plot to black.

plot_surface: Plots the deformed torus surface with:

cmap='plasma': Color map for surface coloring.

edgecolor='none': No mesh lines.

alpha=0.95: Slight transparency.

7. Setting Plot Limits and Hiding Axes

ax.set_xlim([-1.5, 1.5])

ax.set_ylim([-1.5, 1.5])

ax.set_zlim([-1.5, 1.5])

ax.axis('off')

These limit the 3D view range for x, y, z axes and hide the axis grid and ticks for a cleaner look.

8. Adding Colorbar and Title

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

plt.title("Coral Torus Bloom", color='white', fontsize=18)

Adds a color bar to indicate surface value mappings.

Sets the title of the plot with white text.

9. Displaying the Plot

plt.show()

Renders the final 3D visualization.