Phyllotaxis pattern in Python | A unit of Algorithmic Botany

Phyllotaxis pattern in Python | A unit of Algorithmic Botany

Phyllotaxis, the arrangement of leaves on a plant stem, has been a subject of interest both in botany and mathematics due to its intriguing patterns which often resemble spirals. This pattern can be effectively simulated using Python by employing polar coordinates and a bit of mathematical computation, which often relates to the Fibonacci sequence or the golden angle (approximately 137.5 degrees).

To create a visual representation of a phyllotaxis pattern in Python, you can use libraries such as matplotlib for plotting. Here's a basic example to demonstrate this:

  1. Install the Required Library: First, ensure you have matplotlib installed. You can install it via pip if you haven't already:

    pip install matplotlib

  2. Python Script for Phyllotaxis Pattern:

    import matplotlib.pyplot as plt import math def phyllotaxis_pattern(total_points=100, angle=137.5, c=3): plt.figure(figsize=(8, 8)) for i in range(total_points): # Calculating the angle and radius theta = i * math.radians(angle) r = c * math.sqrt(i) # Converting polar coordinates to Cartesian for plotting x = r * math.cos(theta) y = r * math.sin(theta) # Plotting the point plt.plot(x, y, 'o', color='green') plt.axis('off') plt.show() phyllotaxis_pattern()

    In this script:

    • total_points determines how many points will be plotted to form the pattern.
    • angle is the golden angle, and changing this value can produce different patterns.
    • c is a scaling factor for the radius.

  3. Run the Script: When you run this script, it will display a window with the phyllotaxis pattern.

This code generates a simple phyllotaxis pattern using the concept of polar coordinates and plots it using matplotlib. You can experiment with different values of total_points, angle, and c to see how the pattern changes. This algorithm is a basic representation and can be extended or modified for more complex or aesthetically different patterns.

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