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What is a fractal?

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What is a fractal?
Answer
3/27/16 2:12 PM
Hi 

Could anyone offer a description of what a fractal is?

I have read the info here, but still unsure:

http://www.dharmaoverground.org/web/guest/dharma-wiki/-/wiki/Main/MCTB+Fractals

Is it the sense that one is in a stage of a cycle, but somehow that this is contained within a same or different stage of a larger cycle?

Kind of like a cycle within a cycle. Or even a cycle within a cycle within a cycle. 

Thanks 

Barry 

RE: What is a fractal?
Answer
3/27/16 3:07 PM as a reply to Barry D.
Yes, that's it.

A fractal in mathematics is a figure, the product of an algorithm or equation, that has the same dimensions at all scales, infinitely. So fractal phenomena in dharma talk typicaly means that stages are repeated at varying frequencies and intervals, even within themselves. You said it correctly.

RE: What is a fractal?
Answer
3/28/16 3:52 AM as a reply to Chris Marti.
Chris Marti:
Yes, that's it.

A fractal in mathematics is a figure, the product of an algorithm or equation, that has the same dimensions at all scales, infinitely. So fractal phenomena in dharma talk typicaly means that stages are repeated at varying frequencies and intervals, even within themselves. You said it correctly.

Thanks for your response Chris, thats really clearly put.

I guess from a practical point of view it might begin to make mapping difficult, as any given sit can start to have qualities of more than one stage. 

RE: What is a fractal?
Answer
3/28/16 4:12 AM as a reply to Barry D.
To put it in the simplest terms. You might be in a long "dark night" phase in your life (long cycle, lasting maybe weeks), but within a single sit you will be able to experience the other nanas (short cycle, lasting, say, 1h).

Then you might start noticing even shorter cycles. For example, while doing samatha, and in 2nd jhana, you notice a mini-cycle lasting a few minutes, containing some of the dukkha nanas: dissolution, experienced as a loss in clarity; fear, experienced as an increase in heartrate and slight anxiety and restlessness; misery, in the form of a sudden rush of sadness, and so on, until a mini-equamimity which signals full stabilisation of 2nd jhana.

Or you might notice an average-length cycle. Say, within a single day, you notice the increase and decrease in energy, changes in mood, and so on, roughly or strictly in line with the traditional nanas.

So there you go, here you have the example of four cycles, of different time lenghts, one within the other.

RE: What is a fractal?
Answer
3/28/16 5:42 AM as a reply to neko.
Thanks Neko

Nice example, thanks for the illustration.

Using your example, would you say its that overall sense of the Dark Night that may be lasting a number of weeks, that indicates where one is in that path? 

RE: What is a fractal?
Answer
3/29/16 4:58 AM as a reply to Barry D.
Barry Watson:

Using your example, would you say its that overall sense of the Dark Night that may be lasting a number of weeks, that indicates where one is in that path? 

Yes, I would say that the longest cycle is what marks where you are within the path. You could also say that a repeat fruition, non-path level, involves the completion of the the shorter-length cycles, but not the top-level one. A path-level fruition, on the other hand, is when all the cycles synchronise and culminate in a big-ass fruition.

I also remember someone, can't remember whom, trying to apply the four-vipassana-jhanas model to the four paths. Something like:
- first path = first vipassana jhana, effort, and so on
- second path = second vipassana jhana, stabilisation
- third path = dark night: ok this is cool but what next?, territory is vast and confusing, "twelfth path", and so on
- fourth path = equanimity
So, from this point of view, you could talk about a mega-cycle, composed of the four paths, spanning years. It's most probably abusing the maps by this point, but it could be fun to think about it in these terms, and find correspondences for motivation, inspiration, and so on.

RE: What is a fractal?
Answer
3/29/16 2:34 PM as a reply to neko.
Thats great, thanks Neko

It really helps makes sense of my experience. 

Its quite awesome when you think about it. Liked the mega cycle idea :-)

RE: What is a fractal?
Answer
3/29/16 5:03 PM as a reply to neko.
Neko:

Yes, I would say that the longest cycle is what marks where you are within the path. 


Just to stick my nose in, I agree.  I would suggest that the 'long cycles' are actually just afterglow from repeatedly reaching one's cutting edge in short cycles.

So, from this point of view, you could talk about a mega-cycle, composed of the four paths, spanning years


Definitely possible to match the the effort and 'themes' leading up to each technical path to each corresponding, formed jhana.  However, it gets more complex when you incorporate development beyond technical 4th path, once insights related to each nana have been fully integrated, and there is a certain feeling of completion.  IMO this metaphor collapses at that point. 

RE: What is a fractal?
Answer
3/30/16 2:11 PM as a reply to Noah.
Thanks for you comments Noah. 

Are you comments about paths relating to each 'formed Jhana' meaning that each path can be related to a shamata Jhana? 

Like 3rd being connected with the 3rd jhana and so on?

It was interesting to hear your about your sense of how at 4th the insights of the stages have been integrated. Do you mean that you continue to cycle, but it just doesnt reveal anything new?

RE: What is a fractal?
Answer
3/30/16 8:30 PM as a reply to Barry D.
Barry:

Are you comments about paths relating to each 'formed Jhana' meaning that each path can be related to a shamata Jhana?


Yeah.  Leading up to SE corresponds to both the 1st samatha jhana, and nanas 1 through 3.  Working towards 2nd=2nd jhana and 4th nana.  Towards 3rd=3rd jhana and nanas 5 through 11, and 4th=4th jhana (and by default the formless jhanas included within) & 11th nana.

Do you mean that you continue to cycle, but it just doesnt reveal anything new? 


Yeah.

RE: What is a fractal?
Answer
3/31/16 3:35 AM as a reply to Noah.
Noah:

So, from this point of view, you could talk about a mega-cycle, composed of the four paths, spanning years

Definitely possible to match the the effort and 'themes' leading up to each technical path to each corresponding, formed jhana.  However, it gets more complex when you incorporate development beyond technical 4th path, once insights related to each nana have been fully integrated, and there is a certain feeling of completion.  IMO this metaphor collapses at that point. 

Mh, makes sense based on what I have read about it and some glimpses I have had, but can't confirm yet. I will let you know what I think about this when I get tech-fourth. Getting there! Argh! Effort! Attachment! Craving! emoticon