Step by Step solution about How to resolve the algorithm Pythagoras tree step by step in the Python programming language

Details:

1. Importing necessary libraries: The code imports the goto, pu, pd, color, and done functions from the turtle library.

   • goto: Moves the turtle to specified x and y coordinates.
   • pu: Picks up the turtle's pen, stopping it from drawing.
   • pd: Puts down the turtle's pen, allowing it to draw.
   • color: Sets the fill and outline colors.
   • done: Keeps the turtle window open until the user closes it.

2. level function: This is a recursive function that draws a "Koch snowflake" fractal pattern.

   • Parameters:
     • ax, ay: Coordinates of the starting point of the snowflake.
     • bx, by: Coordinates of the ending point of the snowflake.
     • depth: The depth or level of recursion.
   • Logic:
     • If depth is greater than 0, the function calculates three intermediate points (x3, y3, x4, y4, x5, y5).
     • It draws the initial line from (ax, ay) to (bx, by).
     • It then draws the three sides of a triangle: (bx, by) to (x3, y3), (x3, y3) to (x4, y4), and (x4, y4) back to (ax, ay).
     • It picks up the pen and recursively calls level twice:
       • First call: On the left half of the snowflake, from (x4, y4) to (x5, y5) with reduced depth.
       • Second call: On the right half of the snowflake, from (x5, y5) to (x3, y3) with reduced depth.

3. Main code:

   • Setting up:
     • The code sets the fill and outline colors to red and yellow using color.
     • It picks up the turtle's pen using pu().
   • Drawing the snowflake:
     • It calls the level function with starting coordinates (-100, 500) and ending coordinates (100, 500) with a recursion depth of 8.
   • Keeping the window open:
     • It calls done() to keep the turtle window open until the user closes it.

from turtle import goto, pu, pd, color, done

def level(ax, ay, bx, by, depth=0):
    if depth > 0:
        dx,dy = bx-ax, ay-by
        x3,y3 = bx-dy, by-dx
        x4,y4 = ax-dy, ay-dx
        x5,y5 = x4 + (dx - dy)/2, y4 - (dx + dy)/2
        goto(ax, ay), pd()
        for x, y in ((bx, by), (x3, y3), (x4, y4), (ax, ay)):
            goto(x, y)
        pu()
        level(x4,y4, x5,y5, depth - 1)
        level(x5,y5, x3,y3, depth - 1)

if __name__ == '__main__':
    color('red', 'yellow')
    pu()
    level(-100, 500, 100, 500, depth=8)
    done()