Python Turtle Tutorial: Drawing Nested Circles with Recursion

This is a Python program that uses the turtle module to draw a series of nested circles recursively. The program starts by setting up the turtle screen with a title, size, and world coordinates. Then, it defines a function called "draw_circle" that takes as input the coordinates (x, y) of the center of the circle, its radius, and its color, and draws the circle on the turtle canvas.

Next, the program defines a recursive function called "draw_circle_recursive" that takes as input the initial radius of the circles, the direction to draw them in, the number of circles to draw, and an optional color index. The function first draws a circle with the initial radius and color at the center of the screen using the "draw_circle" function. Then, it calculates the radius of the next circle using some trigonometry, and the direction to draw it in by adding an angle based on the number of circles to draw. Finally, the function calls itself recursively with the new radius, direction, and color index.

The program also defines a list of colors to use for the circles and sets the screen tracer to update every 50 steps. It then calls the "draw_circle_recursive" function with an initial radius of 600, 11 circles to draw, and a starting direction of 0. Finally, it updates the screen to show the final result and keeps the turtle screen open until the user closes it.

Overall, this program is a good example of how to use recursion to draw complex shapes and patterns with the turtle module in Python.

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