Y Fractal tree in Python using Turtle

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

In this article, we will draw a colorful Y fractal tree using a recursive technique in Python.

Examples:

Output for depth level: (a) 14 (b) 12

Modules required

turtle: turtle library enables users to draw picture or shapes using commands, providing them with a virtual canvas. turtle comes with Python’s Standard Library. It needs a version of Python with Tk support, as it uses tkinter for the graphics.

Functions used:

• fd(x) : draw the cursor forward by x pixels.
• rt(x), lt(x) : rotates the facing direction of the cursor by x degrees to the right and left respectively.
• colormode(): to change the colour mode to rgb.
• pencolor(r, g, b): to set the colour of the turtle pen.
• speed(): to set the speed of the turtle.

Approach :

• We start by drawing a single ‘Y’ shape for the base(level 1) tree. Then both the branches of the ‘Y’ serve as the base of other two ‘Y’s(level 2).
• This process is repeated recursively and size of the Y decreases as level increases.
• Colouring of the tree is done level wise: darkest in the base level to lightest in the topmost.

In the implementation below, we will draw a tree of size 80 and level 7.

from turtle import *


speed('fastest')

# turning the turtle to face upwards
rt(-90)

# the acute angle between
# the base and branch of the Y
angle = 30

# function to plot a Y
def y(sz, level):

    if level > 0:
        colormode(255)

        # splitting the rgb range for green
        # into equal intervals for each level
        # setting the colour according
        # to the current level
        pencolor(0, 255//level, 0)

        # drawing the base
        fd(sz)

        rt(angle)

        # recursive call for
        # the right subtree
        y(0.8 * sz, level-1)

        pencolor(0, 255//level, 0)

        lt( 2 * angle )

        # recursive call for
        # the left subtree
        y(0.8 * sz, level-1)

        pencolor(0, 255//level, 0)

        rt(angle)
        fd(-sz)


# tree of size 80 and level 7
y(80, 7)

Output :