The image below was created using the current release of the visualization program 3D-XplorMath (available
by clicking here. ) It is an image of the Feigenbaum Tree, on which is superimposed a numerically computed density function that we believe represents the invariant measure of the iteration with the current parameter choice. We would like to document this carefully---we think we have computed the density correctly, however we have not seen this measure mentioned elsewhere and do not know any discussion of how to compute such a measure. (In particular,the obvious Googling does not turn up anything.) Does anyone know where to
find more about this?