Rose Curve Pattern using python

 

import numpy as np

import matplotlib.pyplot as plt

a=5

k=7

theta=np.linspace(0,2*np.pi,1000)

r=a*np.cos(k*theta)

x=r*np.cos(theta)

y=r*np.sin(theta)

plt.figure(figsize=(6,6),facecolor="black")

plt.plot(x,y,color='magenta',linewidth=2)

plt.axis('off')

plt.title(f"Rose curve pattern(k={k})",color="white",fontsize=14)

plt.show()

#source code --> clcoding.com

Code Explanation: 

Step 1: Import Required Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy (np): Used for numerical computations (e.g., generating angle values for the curve).

matplotlib.pyplot (plt): Used for plotting the Rose Curve.

Step 2: Define Parameters for the Rose Curve

a = 5  

k = 7  

a (Amplitude): Controls the size of the rose curve.

k (Frequency): Defines the number of petals in the Rose Curve.

If k is odd, the Rose Curve has k petals.

If k is even, the Rose Curve has 2k petals.

Step 3: Generate Theta Values (Angle in Radians)

theta = np.linspace(0, 2 * np.pi, 1000)

theta represents the angle in radians, ranging from 0 to 2π (a full circle).

np.linspace(0, 2 * np.pi, 1000) generates 1000 equally spaced values between 0 and 2π, ensuring a smooth curve.

Step 4: Compute r (Polar Radius) for the Rose Curve

r = a * np.cos(k * theta)

This is the polar equation of the Rose Curve:

r=a⋅cos(kθ)

a (5) scales the curve, affecting the size.

k * theta determines the oscillation frequency of the petals.

Step 5: Convert Polar Coordinates to Cartesian Coordinates

x = r * np.cos(theta)

y = r * np.sin(theta)

Since matplotlib plots in Cartesian coordinates (x, y), we convert from polar to Cartesian:

x=r⋅cos(θ)

y=r⋅sin(θ)

This transforms the radius (r) and angle (theta) into X, Y coordinates.

Step 6: Set Up the Figure for Plotting

plt.figure(figsize=(6,6), facecolor="black")

figsize=(6,6): Creates a square figure (6x6 inches).

facecolor="black": Sets the background color to black for a stylish effect.

Step 7: Plot the Rose Curve

plt.plot(x, y, color='magenta', linewidth=2)

plt.plot(x, y, color='magenta', linewidth=2)

x, y: The calculated coordinates of the Rose Curve.

color='magenta': Sets the line color to magenta (pinkish-purple).

linewidth=2: Controls the thickness of the curve.

Step 8: Hide Axes for a Clean Look

plt.axis("off")

Hides the X and Y axes to make the design look more artistic.

Step 9: Add a Title

plt.title(f"Rose Curve (k={k})", color="white", fontsize=14)

Displays a title:

Uses f"Rose Curve (k={k})" to dynamically show the value of k in the title.

color="white" makes the title white for visibility on a black background.

fontsize=14 sets the font size.

Step 10: Display the Plot

plt.show()

Displays the final Rose Curve plot.