A close cousin of the Mandelbrot set is the Julia set. Read about the Julia set and then modify 8.07_Mandelbrot.py to produce a Julia set. Fractals are a very interesting topic to study and a lot of the maths behind them is still unexplored.  Besides the fact that they are beautiful to look at, they are also used in a lot of practical applications. See https://en.wikipedia.org/wiki/Fractal#Applications_in_technology.

If fractals pique your interest, you can also take a look at other variants of the Mandelbrot set such as the Magnet 1 fractal and Buddhabrot. 

If you are interested in learning more about chaotic behavior, try to plot Hénon’s Function on a Tkinter canvas.

We modeled a spring pendulum and it worked in a deterministic manner. However, adding two pendulums together to form a double pendulum creates a dynamic system that is chaotic. Even though such systems follow the ordinary differential equation, the net outcome may vary immensely, even for a very small change in the initial condition. It may be worth trying to model a double pendulum by modifying our spring pendulum.

We used the built-in odeint method from scipy. However, we could have written our own variation using either the Euler's method or Runge-Kutta method. You can read more about these numerical methods for approximating ordinary differential equations over here:  https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations.

If neat or intriguing visualizations looks like a fun thing to do,  here are a few more interesting canvas projects that you can undertake: Barnsley fern, the cellular automata, the Lorenz attractor, and simulating tearable cloth with verlet integration.

Ray tracing is another powerful but very simple to implement 3D rendering technique that can be easily implemented in about 100 lines of code.