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Description
Turning the Mandelbrot set inside out

or

When zero and infinity alter their places

Full view please for the illustration

The upper half of the illustration is generated by the dynamical process z -> z^2 + c when the variable “z” is initiated to zero and “c” varies with the pixels (c = # pixels). The black part is the Mandelbrot set and is constituted of those “c” for which “z” under iteration stays forever within a radius of 2 from the center of the dynamical (z-) plane. The surrounding colors are settled according to how many iterations (how many times the variable “z” has to pass the loop) for the corresponding “c” before “z” passes a radius of at least two, in this image 10, and thus escapes to infinity. But all of this is much more clearly described in articles 1 – 9 in my Chaotic series of fractal articles.

Now we shall perform a little joke. We let the infinity and zero on the parameter plane (the c-plane) alter their places. That means we turn the parameter plane (containing the M set and the surrounding level sets) inside out by instead iterating z -> z^2 + 1/c. The result is shown in the lower part of the illustration, the black set is the Inverse Mandelbrot set. that now surrounds the level sets in the central part of the image. Note that there are one-to-one correspondences between every point in the upper and lower planes if they are extended to include the infinity. In fact the border of the sets are exactly similar, the branches of the Inverse M set containing copies of ordinary M set in exactly the same way the ordinary M set does. The double arrowhead lines show this.

This “inside-out-process” throw away the “zero” in the upper motive to infinity’s infinity in any direction in the lower image and, at the same time, catches the infinity’s infinity in any direction in the upper image and places it on the well defined spot “at infinity” in the lower image. But all this has partly to do with the mysteries of zero divides, see my preceding journal The mysteries of zero divides

And when the space is turned inside out, the whole universe will be situated inside you

Description
Turning the Mandelbrot set inside out

or

When zero and infinity alter their places

Full view please for the illustration

The upper half of the illustration is generated by the dynamical process z -> z^2 + c when the variable “z” is initiated to zero and “c” varies with the pixels (c = # pixels). The black part is the Mandelbrot set and is constituted of those “c” for which “z” under iteration stays forever within a radius of 2 from the center of the dynamical (z-) plane. The surrounding colors are settled according to how many iterations (how many times the variable “z” has to pass the loop) for the corresponding “c” before “z” passes a radius of at least two, in this image 10, and thus escapes to infinity. But all of this is much more clearly described in articles 1 – 9 in my Chaotic series of fractal articles.

Now we shall perform a little joke. We let the infinity and zero on the parameter plane (the c-plane) alter their places. That means we turn the parameter plane (containing the M set and the surrounding level sets) inside out by instead iterating z -> z^2 + 1/c. The result is shown in the lower part of the illustration, the black set is the Inverse Mandelbrot set. that now surrounds the level sets in the central part of the image. Note that there are one-to-one correspondences between every point in the upper and lower planes if they are extended to include the infinity. In fact the border of the sets are exactly similar, the branches of the Inverse M set containing copies of ordinary M set in exactly the same way the ordinary M set does. The double arrowhead lines show this.

This “inside-out-process” throw away the “zero” in the upper motive to infinity’s infinity in any direction in the lower image and, at the same time, catches the infinity’s infinity in any direction in the upper image and places it on the well defined spot “at infinity” in the lower image. But all this has partly to do with the mysteries of zero divides, see my preceding journal The mysteries of zero divides

And when the space is turned inside out, the whole universe will be situated inside you