Similarity between Henon attractor and logistic map? I noticed that layering Henon attractor images with avalue=1 and bvalues from -0.2 to 0.3 looks like  a distorted version of the logistic map.
In the image below you can see the layered images (left).
After that I tried to accentuate the first "branches" (right)

Is there any way to explain this similarity?
 A: There is a way to explain the similarity. According to wikipedia, the Feigenbaum constant is tied to the bifurcation of all chaotic maps:
http://en.wikipedia.org/wiki/Feigenbaum_constants
"Feigenbaum originally related the first constant to the period-doubling bifurcations in the logistic map, but also showed it to hold for all one-dimensional maps with a single quadratic maximum. As a consequence of this generality, every chaotic system that corresponds to this description will bifurcate at the same rate. It was discovered in 1978.[1]"
A: Henon gives the canonical definition for the map named in his honor in a 1976 publication in Communications in mathematical physics:
$$x_{n+1} = y_n +1 - a*x_n^2 \\
y_{n+1} = b*x_n$$
Substituting, we get $x_{n+1} = b*x_{n-1} + 1 - a*x_n^2$. If $b = 0$, we have $x_{n+1} = 1 - a*x_n^2$, which is just a quadratic map, of which the best known case is the logistic map. The Feigenbaum stuff is important and general, but in this case, the logistic map is simply embedded within the action of the Henon map.
