Today I am messing with the Bogdanov Map (sourced from this fun wikipedia list of chaotic maps) which for some parameters $\varepsilon$, $\mu$, $k$ maps $(x_n, y_n)$ to:

\[x_{n+1} = x_n + y_{n+1}\] \[y_{n+1} = y_n + \varepsilon y_n + k*x_n(x_n-1) + \mu x_ny_n\]

The map seemed to be sending things off to very large numbers; so, here I am in each step updating the value modulus the canvas width and height and taking the absolute value. I am choosing random values in $(-3,3)$ (or exactly $0$) for $\varepsilon$, $\mu$, and $k$ and iterating on a single starting point in the middle of the canvas (note the chosen values are printed with console.log for now). I would like to play with this more and see what parameter values yield interesting results (or see what else I can do with it), but don’t have time today. Still, this has convinced me that playing around with different sorts of chaotic maps would be fun in the future.

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