Visualizing Chaos With Sound

The bifurcation diagram of the logistic map given in the figure plots the fixed population of bugs on the ordinate as a function of the growth rate on the abscicca. In the dark regions, the system is chaotic.


The Logistics Map (210k)


Instead of just plotting the fixed population of bugs, we now use a grid to find out how often the population is in a given range. In the following plots the x-axis represents the size of the population and the y-axis how often the population had this value.


Slices of the bifurcation map for growth rate m=2.0, 3.2 and 3.6

To visualize the bifurcation map with sound, we create these plots for the whole range of the growth parameter and interpret them as a fourier spectrum. In other words, when there is only one population there will be just one frequency played, yet the value of the frequency will increase as the population increases. When there are two populations, there are two frequencies played, and when there is chaos many frequncies are played. In fact, there is at least some poetic justice here since chaotic motion is the combination of many types of periodic motions.
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