This simulation calculates the logistic map with adjustable high resolution. It is recommended to increase the simulation window to full screen size to see the details.
When the simulation is opened, the abscissa range is defined by rmin = 0.740 and rmax = 1. This covers the whole bifurcation range. With Start the calculation begins, for a resolution of 2000 points in the r range.
Using two sliders rmin and rmax can be varied (best done after Stop when the full pattern is visible) to define a zoomed cutout of the total bifurcation range. This zoomed range will be recalculated with 2000 r points again at Start. Resolution is always 2000 r points for the defined interval. This way one can explore the intricate pattern in great detail. With very high resolution the values for rmin < rmax can be defined in two number fields next to the sliders.
To return to the default setting, the sliders are reshifted to their extreme positions.
At default the first 1000 iterations are not shown, but the following 250 ones. Therefore each r value can lead to a maximum of 250 points in the ordinate direction. At this number of displayed iterations the overlay structure built by parabolas of increasing order can be well recognized by empty places in the "filled" band where no bifurcations are visible.
In the number field supressed the number of suppressed iterations can be changed. At low numbers (10), one will notice a marked scatter as influence of the random initial values. At very high values (max. 100 000) no scatter is visible. The scatter at 1000 suppressed iterations is well visible at the bifurcation points for high r resolution. It will be different for different runs because of the random generation of the initial values.
For a higher number of iterations the "filled" bands fill up more and more. At 100 000 iterations they would appear densely filled. The bifurcations in the "empty" bands stay the same.