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      Mandelbrot/Julia combination, jnana yoga

      I assume most people who read and post here have seen images of the Mandelbrot set. This is generated by the equation z(n+1) = z(n)*z(n) + c, where z and c are complex numbers, and z(0) = 0. If you also vary z(0), you get a four dimensional object that I find metaphorically interesting in relation to dream experiences of what seem to be higher or parallel worlds. I've never seen anyone try to form a projection of a 3-dimensional cross section of that set. But people do form images of the Julia sets, which are from keeping c constant and varying z(0). The free software at Downloads | Fraqtive displays Julia sets depending on where your mouse arrow is on a Mandelbrot image. So by moving your mouse arrow in a curve and paying attention to what's happening, you can see the structure of how the Julia sets are connected in 4 dimensions.

      Some quasi-Theosophists have a concept of a 'dividing of the way', where at certain astrological junctures the souls in our world get partitioned into two groups and continue their re-existences on separate worlds for the next cycle. If you zoom in on the Mandelbrot set, and draw the mouse arrow across a thin filament of it, you can see something like this in the Julia sets. Structures in two sides of the set join, exchange parts in a complex way, then separate again. This is easiest to see when zoomed in near the far left tip of the Mandelbrot set where it looks 'hairier'. A person can see other interesting properties, such as two objects that are close together and joined by a curve that has infinite length.

      I think that most lucid dreamers should be able to enrich their experiences with more exposure to these kinds of topological ideas, because it provides more tools for forming images out of the more subtle things one experiences in dreams. It has also been essential to a few paranormal experiences I've had in waking life.

      Another thing that has been valuable to me in this context is discovering that I can move my identity around. Part of how I learned that is by reading dialogs with Ramana Maharshi. I don't buy into his theology, but if you practice his meditation it points to deeper parts of yourself that you might not have been aware of before. Or, if you're like me and you don't practice the meditation, you still get some of the same effect just by mind-meld when reading about it. For some people, one way to do that would be by watching tapes by his successor Gangaji on YouTube. Discovering more of my capacity to feel is how my experiences with astral projection, precognition, shared thought, and other related things become possible. That discovery came as a result of this sort of thought.

      Of course this won't be everyone's cup of tea, but I'm just throwing it out there as one way to get these kinds of experiences that doesn't involve hallucinogenic drugs. In my mind the movement of identity pointed to by Ramana Maharshi (or any similar guru) is closely analogous to the sensory movement that occurs during astral projection. And the 'fractal' mathematical ideas can introduce you to ways of experiencing reality that aren't locked into the usual 3-D Euclidean metric.

      If you install and run the Mandelbrot program, you'll want to go to View->Properties->Advanced-Settings and maximize the calculation depth and detail level. Otherwise you'll get boring, 80's quality pictures. After that, you zoom in on by clicking and moving the mouse. The Julia set is in the pane on the right.
      Last edited by shadowofwind; 02-04-2012 at 09:55 PM.

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