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–probably better suited for the research area, because not yet proven —
The equivalent to Inflation/Big Bang in the mandelbrot set is a zoom into the “empty” infinite plane (power law, which is everywhere around us, see winiwarter) until you suddenly reach the number space between -2 and +1 of the mandelbrot set. It blows up from a single point, an infinitely dense singularity.
as soon as it “fills the screen” everything is different, you see new rules and patterns, as emergent consequence of the basic formula.
before there was nothing – afterwards theres everything, repeating in self similar patterns over and over to infinity while zooming.
A fixed zoom speed into the M-set is the equivalent to the cosmological constant.
from Andrej Lindes “New Inflation”-Theory Wikipedia entry:
Thus our world, instead of being a single spherically symmetric expanding balloon, becomes a huge fractal, an inflationary multiverse consisting of many different pocket universes with different properties. This provided a simple scientific interpretation of the cosmological anthropic principle: Our world may consist of different parts, but we can live only in those parts of the multiverse which can support life as we know it.
These ideas did not attract much attention at that time, in part because the anthropic principle was very unpopular, in part because the new inflationary scenario did not quite work and was replaced by the chaotic inflation scenario. However, in 1986 Linde found that in many versions of the chaotic inflation scenario, the process of exponential expansion of the universe also continues forever in some parts of the universe. Linde called this process eternal inflation.
(to check: does he mention fractals in this