Rediscovering Fracal Visualization

As I was cleaning up old files on my server I came across several old college projects. One of them contained several Java applets for fractal visualization — circa 2002. While I cringed slightly at the writing I was impressed with the mathematics that I have since forgotten! Like, what the hell is IFS and why am I calling it non-deterministic? Apparently, it’s a random iteration algorithm where I assign probabilities to each function in an IFS (Iterative Function System). An IFS is a set of affine transformations, and in this case each transformation is assigned a probability– Obviously!

There’s also some classic Mandelbrot and Julia Sets. Since several years have passed since this was all created, I’m interested in doing similar visualizations and not using Java. Java never really did catch on for client-side web applications. Although I do like the idea of doing the number crunching on the client side :) Maybe I’ll try it in Flash…

If interested, here is what is left of the old fractal page:


“If the doors of perception were cleansed every thing would appear to man as it is, infinite.”
– William Blake

Taking notes during an altered state of consciousness:

I go deep. Voices point me towards what first appears as an abyss. Further down it opens up. Amazed at the overwhelming detail of what I am seeing, I wonder what I am not seeing. An infinite number of paths each with limitless depth — the experience reminded me of zooming in on a fractal.

Breaking through that glowing membrane … I go deeper … outside of my conscious mind. It is dark as there is no visual representation to adequately describe the experience. Like driving late at night only the road before me is illuminated yet the ever present feeling of the infinite abounds. And what can only be described as children were pointing me towards a glowing opening. As I thought “follow my happiness”, they seemed to agree, “yes, that way”.

At any point I could have stopped, any path, any where — all of them so rich in details and life — the focus of my attention seems to drive me forward. Details unfold as I go. Dark, but never empty and not frightening.

And so I went, onward through another layer, darkness at first and blinding light seemed to mix together. I came upon two distinct windows of blinding light, my eyes. I’m looking out through them but the feedback is recursive. They are connected to me through this path, this loop I have just created — I am seeing “me” from the other side but through my own eyes.

My body, I realize, is not a temple — it is merely a vehicle from which I am aware; finite awareness of an infinite space, like zooming in on the edges of a fractal.

I stand up. Assuming my experience is at an end — the world looks the same. Only it is not. I close my eyes and see… Strands of consciousness and thought, glowing fibers criss-crossing into infinity. I move from strand to strand.

I decide to exercise — meditate through tai chi. Simple stretches and moves. My eyes closed — everything seems to move with me, it is not me that is moving, it is the universe moving through me; I am only an awareness of the movement of the universe. It seems to dance and rearrange itself at my every whim. Conscious awareness of a finite piece of an infinite universe.

I was momentarily worried that I just tied my brain in a knot. I recognized that was just another filter, trying to map the experience into terms I can rationalize… like trying to imagine a hypercube in 3-dimensions. It seems to cross through itself in impossible ways, but once you realize what it is — it’s just your mind rationalizing it in 3-dimensions that makes it seem impossible.

I realize it is only our perception; the ultimate filter on the infinite. The epiphany was when I realized it all comes back to my awareness in life — that I am just this singular awareness of a finite perception of the infinite — and where in past meditation I did not see, I realized that the movement was the key. You can see and experience the boundless energy of the universe, but letting it move is amazing. Life becomes the movement of the universe through you — things you are thinking come and go into your life — exactly like zooming into the edges of a fractal.

North Shore Kauai

If you’re ever in Kauai, get as far away from paved roads as you can. It seems like every dirt road makes its way to an amazing beach. My desire for hiking has been betrayed by my desire to lounge in the water.

Nearly everywhere you go is the perfect hideaway to just relax and get away. Not a worry in the world; just soft sand, cool air, and a warm sun that makes you want to melt away.

And yet there is a bizarre sensation that it is unreal. The confines of a beautiful oasis constantly distracting. An amazing facade drawing you into a quasi-fulfilled state of happiness. The human spirit, I suspect, needs a little chaos to truly flourish. I wonder if that volcano will ever be active again?