# Pictorial Renormalization Group - Demo 2

## a=2.9

For *a=2.9* the fixed point has evolved to a value *x>0.5*. While the iterations are running, click somewhere in the plot to start a new iteration with initial condition the value of *x* at the mouse position.

All initial conditions lead to an orbit that converges to the fixed point which is *stable*. The orbits now spiral into the fixed point, corresponding to the negative slope of *f* here (successive deviations from the fixed point change sign as well as shrink).

The stability of the fixed point is easily seen going to the second iterate of the map *f*^{ 2}(x)=f(f(x)) by putting *nf=1*.

The slope of the curve at the intersection with the diagonal is less than unity, and the orbit staircases in to the fixed point.

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Last modified Sunday, December 12, 1999

Michael Cross