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.

back to the genuary index

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