Perhaps a silly question but assuming Gottfried and Jay plot iterations of type sexp^[k](x) for x values near the real line ...
Then why do these contours of iterations not intersect ?
I mean why do we not get contours like here :
http://math.eretrandre.org/tetrationforu...hp?tid=499
Afterall iterations of sqrt(2)^x are just as chaotic as those of exp(x) or not ?
Or does this occur in the white space ?
What happens to secondary and higher fixpoints ... are they the " cut-in's " of the white space / fractal / branch ?
I note that b^x = b^(x+period)
but I do not see that at the plots.
My guess is it ( b^(x+period) is replaced by b^x + period , and this explains some missing contour intersections / merges / discontinuity.
I think f ' (2) / f ' (4) is involved.
EDIT : yes I understand the iterations are of IMAGINARY height and that PARTIALLY explains some things like the circle shapes and locally not intersecting ... but still.
regards
tommy1729
Then why do these contours of iterations not intersect ?
I mean why do we not get contours like here :
http://math.eretrandre.org/tetrationforu...hp?tid=499
Afterall iterations of sqrt(2)^x are just as chaotic as those of exp(x) or not ?
Or does this occur in the white space ?
What happens to secondary and higher fixpoints ... are they the " cut-in's " of the white space / fractal / branch ?
I note that b^x = b^(x+period)
but I do not see that at the plots.
My guess is it ( b^(x+period) is replaced by b^x + period , and this explains some missing contour intersections / merges / discontinuity.
I think f ' (2) / f ' (4) is involved.
EDIT : yes I understand the iterations are of IMAGINARY height and that PARTIALLY explains some things like the circle shapes and locally not intersecting ... but still.
regards
tommy1729