((c
2 + c)
2 + c)
2 + c ¼ (c
2 + c)
2 + c, representing 3 and 2 iterations of the Mandelbrot
formula on the left and right hand side, respectively. But this location may have more
to teach us than most, because it is an archetypal example of principles that apply in a
more complex way to a broad class of Misiurewicz points in M, and these points
appear to be the most relevant places in M to Physics. If we highlight where the
iterand magnitude monotonically diminishes over 3 values, revealing the Mandelbrot Butterfly, this spot is the boundary for a circular disc around a mini-M figure,
extending all the way down to (À2, 0i). This disc is the largest of a vast family of
discs around the periphery of the Butterfly figure, near the Misiurewicz points—
denoting basins of attraction. This particular basin of attraction appears to simulate
gravity, denoting r G the radius of gravitation (confluence in Fig. 7.2 and disc near
base in Fig. 7.3).
The algorithmic nature of M and its associated figures is what allows us to show
the wings and discs of the Mandelbrot Butterfly figure, but it also lets us suppress
lower-order solutions to strip away layers of the Butterfly’s form and see what is
underneath. Ergo, we can observe the condensation process in more detail, by
removing the largest disc and seeing what higher-order solutions are doing in that
same region of M. One might ask what the Mandelbrot Set could possibly have to do
with the Physics of gravity, black holes, and quantum condensation—apart from
some nice analogies with physical processes to stimulate creative thought. Indeed,
the author took a philosophical view of this work for many years, and had little
communication with academics about it—apart from phone conversations with
Benoit Mandelbrot some 30 years ago. But with the discovery in 1998 of the
accelerating expansion of the universe (Perlmutter et al. 1998; Reiss et al. 1998), it
became apparent to the author that what was being learned closely matched predictions based on features of the Mandelbrot Set. Ten years later, the author first
presented these insights at the second crisis in Cosmology conference (Dickau
Fig. 7.1 The Mandelbrot Set illustrates Cartan’s G 2 rolling ball analogy in its major geometry
72
J. J. Dickau
2 + c)
2 + c)
2 + c ¼ (c
2 + c)
2 + c, representing 3 and 2 iterations of the Mandelbrot
formula on the left and right hand side, respectively. But this location may have more
to teach us than most, because it is an archetypal example of principles that apply in a
more complex way to a broad class of Misiurewicz points in M, and these points
appear to be the most relevant places in M to Physics. If we highlight where the
iterand magnitude monotonically diminishes over 3 values, revealing the Mandelbrot Butterfly, this spot is the boundary for a circular disc around a mini-M figure,
extending all the way down to (À2, 0i). This disc is the largest of a vast family of
discs around the periphery of the Butterfly figure, near the Misiurewicz points—
denoting basins of attraction. This particular basin of attraction appears to simulate
gravity, denoting r G the radius of gravitation (confluence in Fig. 7.2 and disc near
base in Fig. 7.3).
The algorithmic nature of M and its associated figures is what allows us to show
the wings and discs of the Mandelbrot Butterfly figure, but it also lets us suppress
lower-order solutions to strip away layers of the Butterfly’s form and see what is
underneath. Ergo, we can observe the condensation process in more detail, by
removing the largest disc and seeing what higher-order solutions are doing in that
same region of M. One might ask what the Mandelbrot Set could possibly have to do
with the Physics of gravity, black holes, and quantum condensation—apart from
some nice analogies with physical processes to stimulate creative thought. Indeed,
the author took a philosophical view of this work for many years, and had little
communication with academics about it—apart from phone conversations with
Benoit Mandelbrot some 30 years ago. But with the discovery in 1998 of the
accelerating expansion of the universe (Perlmutter et al. 1998; Reiss et al. 1998), it
became apparent to the author that what was being learned closely matched predictions based on features of the Mandelbrot Set. Ten years later, the author first
presented these insights at the second crisis in Cosmology conference (Dickau
Fig. 7.1 The Mandelbrot Set illustrates Cartan’s G 2 rolling ball analogy in its major geometry
72
J. J. Dickau