Unfortunately, I somehow am not able to keep myself from presenting just a few of the basics of fractal theory here, particularly as it relates to Bill’s model. There is also something exceedingly universal about the pattern that I am about to present, and resonances of it are found back as far as there is recorded human history, religion and art.
If you consider the first 360 degrees of a sine wave (like a rounded capital italic “N” that has been tilted just a bit to the right), you will notice that is starts at zero, goes up in a hill-like way, peaks, descends below where it started in a valley-like way, bottoms out, and then returns to the same level at which it began but yet farther along.
Were one walking on this curve, one would have to make effort to climb up the hill. One would then have a spectacular view and a great sense of accomplishment. One might then try to keep walking up to get more of this, but end up sliding down the other side of the hill, farther down in fact than where one began. And yet, this is still progress, and could even be somewhat thrilling and even effortless with the right attitude. Just when one gets to the very bottom, trapped in the darkest part of the pit, by finally coming to rest at the absolute bottom the upward motion begins to happen naturally, and one returns to where one was, ground zero, and yet farther on at the same time. A cycle is complete and yet begins again endlessly.
This easily correlates with the first four vipassana jhanas, as well as many other obvious cycles such as those of the sun and seasons, etc. For those trying to correlate the maps of the progress of insight with those of Tantra’s Five Buddha Families or those of any number of pagan and nature-based traditions, this should prove most helpful. The first vipassana jhana is climbing up the hill, eager beginnings, hard work, dawn, Spring, East, etc. The second vipassana jhana is the giddy high of accomplishment at the top of the hill, high noon, Summer, South, etc. The third vipassana jhana is the exhilarating and yet scary fall far down the other side into a cool and shadowy valley, dusk and nightfall, Autumn, West, etc. The fourth vipassana jhana is coming to rest regardless of where one is and returning to one’s origin naturally, the cool of the dead of night and early morning, Winter and the promise of Springtime, the coming of a new year at the end of the old, a time of rest, completion and renewal, North. The correlations with the stages of insight are thus obvious. One may also correlate this with some of the models of awakening, particularly the Four Path Model and the Simple Model of awakening, both of which will be explained later.
Interestingly, one may begin to see a full cycle of each of these stages in each of the four vipassana jhanas as well, with each peak and valley adding or subtracting from the position of the greater wave it is an aspect of. For all you incurable model geeks, try plotting y=sin(x)+0.25sin(4x) from x=0 to 2pi on a graphing program. You have my sympathy. The x-axis is the jhanas and sub-jhanas, from 1.1 to 4.4, or 1.1.1 to 4.4.4 if you want to go into sub-sub-jhanas. Unfortunately, what goes on the y-axis would be the subject of a book longer than this one and would read like the most difficult works of Aleister Crowley. In short, the possible complexity of this model is endless and it is no substitute for practice. Try not to become an arrogant twit like I did when I began to figure all this stuff out. Esoteric map theory won’t win you any friends.
I have spent way too much time thinking about the fractals and modeling in my own practice. In my insecure moments, I have considered showing off and writing a book that detailed the hundreds of little parallels and patterns that I have noticed over the years, how this tiny little stage of some vipassana sub-jhana mirrored or was an inversion of another aspect of some other little stage of some other sub-sub-jhana, but I couldn’t come up with any practical use for it at all. If you do the technique, you will see all of this and more. If not, reading about it won’t help you. It’s just another content trap, but a seductive one for us pseudo-intellectuals. On the other hand, Khabbala seems to have made related permutations into meditation itself, and those who are particularly inclined to this sort of analysis might want to try taking it as a vehicle for going beyond it. Also, guess where the complex geometric Tibetan Mandalas that are supposed to be pictures of the Mind or the Universe come from? Bingo!