A modified Edmund Harriss type plot of a Collatz orbit.

collatz_harriss_adjusted.py

import math
import numpy as np
import matplotlib.pylab as plt


def harriss_plot_adj(
    ax, n, 
    
    angle=11.45, twist=1.8,  # Controls the odd/even turn angles
    
    decay=.999,   # Rate of decay of segment length
    lw=10,        # Initial segment thickness
    taper=0.99,   # Rate of decay of segment thickness/alpha
    
    *args, **kwargs
):
    
    """A modified Harris visualisation of the orbit of a given Collatz number, n.
    
    Args:
    
    ax:    The plotting axis (matplotlib).
    n:     The Collatz number whose orbit we wish to visualise.
    angle: The line segments for even numbers use -angle (clockwise)
    twist: The odd numbers use an angle of angle*twist (anti-clockwise).
    decay: The rate of decay of the length of the line segments.
    lw:    The thickness of the linsegents at the root (1).
    taper: The rate of decay of the thickness (and alpha) of the line segments.
    
    """
    # Convention is that 1 is the root, so reverse the orbit.
    orbit = collatz_orbit(n)[::-1]
    
    prev_x, prev_y, heading = 0, 0, 0
        
    # For each element in the orbit ...
    for i, o in enumerate(orbit):
        
        # Update the current heading based on the even/odd turn angle.
        heading += turn_angle(o, angle=angle, twist=twist)
                
        # Calculate the new (x,y) ...
        new_x = prev_x + ((decay**i)*math.cos(math.radians(heading)))
        new_y = prev_y + ((decay**i)*math.sin(math.radians(heading)))
        
        # Plot the current line segment after setting the width and alpha
        width = lw*(taper**i)   # Segments closer to the root (1) are thicker.
        alpha = taper**i        # Segments closer to the root are darker/less transparent.
        ax.plot([prev_x, new_x], [prev_y, new_y], lw=width, alpha=alpha, *args, **kwargs)
        
        # Update the prev (x, y).
        prev_x, prev_y = new_x, new_y