How to resolve the algorithm Peano curve step by step in the Python programming language

Published on 12 May 2024 09:40 PM
#Python

How to resolve the algorithm Peano curve step by step in the Python programming language

Table of Contents

Problem Statement

Produce a graphical or ASCII-art representation of a Peano curve of at least order 3.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Peano curve step by step in the Python programming language

This Python code uses the turtle graphics library to generate a Peano curve, which is a space-filling curve that fills a square in a continuous path.

The code starts by importing the turtle library and defines a global variable called stack to keep track of the current recursion stack depth. The peano() function takes an optional parameter iterations that specifies the number of iterations to perform.

Inside the peano() function, a turtle named ivan is created and an app window is set up. The size of each step walked by the turtle is set to walk, and a function screenlength() is defined to calculate the appropriate screen size for the given number of iterations.

The "magic" of the Peano curve is implemented in two recursive functions, step1() and step2(). These functions use a combination of forward and turn commands to guide the turtle through the curve, and they call each other recursively to create the complex pattern.

The stack variable is used to track the depth of the recursion stack, which provides a visual representation of the curve's complexity.

Finally, the peano() function calls step2() with the given number of iterations, and the turtle graphics window is displayed using tt.done().

After the drawing window is closed, the code uses the pylab library to plot the stack variable, which shows the stack depth at each step of the recursion. This plot provides insights into the recursive nature of the Peano curve.

Source code in the python programming language

import turtle as tt
import inspect

stack = [] # Mark the current stacks in run.
def peano(iterations=1):
    global stack

    # The turtle Ivan:
    ivan = tt.Turtle(shape = "classic", visible = True)


    # The app window:
    screen = tt.Screen()
    screen.title("Desenhin do Peano")
    screen.bgcolor("#232323")
    screen.delay(0) # Speed on drawing (if higher, more slow)
    screen.setup(width=0.95, height=0.9)

    # The size of each step walked (here, named simply "walk"). It's not a pixel scale. This may stay still:
    walk = 1

    def screenlength(k):
        # A function to make the image good to see (without it would result in a partial image).
        # This will guarantee that we can see the the voids and it's steps.
        if k != 0:
            length = screenlength(k-1)
            return 2*length + 1
        else: return 0

    kkkj = screenlength(iterations)
    screen.setworldcoordinates(-1, -1, kkkj + 1, kkkj + 1)
    ivan.color("#EEFFFF", "#FFFFFF")


    # The magic  \(^-^)/:
    def step1(k):
        global stack
        stack.append(len(inspect.stack()))
        if k != 0:
            ivan.left(90)
            step2(k - 1)
            ivan.forward(walk)
            ivan.right(90)
            step1(k - 1)
            ivan.forward(walk)
            step1(k - 1)
            ivan.right(90)
            ivan.forward(walk)
            step2(k - 1)
            ivan.left(90)
    def step2(k):
        global stack
        stack.append(len(inspect.stack()))
        if k != 0:
            ivan.right(90)
            step1(k - 1)
            ivan.forward(walk)
            ivan.left(90)
            step2(k - 1)
            ivan.forward(walk)
            step2(k - 1)
            ivan.left(90)
            ivan.forward(walk)
            step1(k - 1)
            ivan.right(90)

    # Making the program work:
    ivan.left(90)
    step2(iterations)

    tt.done()

if __name__ == "__main__":
    peano(4)
    import pylab as P # This plot, after closing the drawing window, the "stack" graphic.
    P.plot(stack)
    P.show()

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