Far from being a mere curiosity, the phenomena of self-similarity and recursiveness have been noticed by Buddhist writers such as Samanera Bodhesako. He wrote in his essay "The Buddha and Catch-22":
And the reason for this, the Buddha informs us, is because of avijjā, or ignorance. But avijjā is not a mere absence of information; it is a refusal to see what is at all times there to be seen. It is not failure to see one particular thing among other particular things, but a radical refusal to see the way all particular things are, and in this respect it is as great a modifier as death — indeed, the two are (so the Buddha tells us) inseparable. The dependent arising formulation says, in summary, “With ignorance as condition, ageing and death, sorrow, lamentation, pain, grief, and despair come into being.”
The deluded person, in refusing to see the nature of all things, refuses also to see the nature of his refusal to see (which is also a thing). That is, he refuses to see delusion. Thus, by denying itself delusion sustains itself. This is stated in the Suttas (e.g. Sammāditthi Sutta, M. 9) as follows:
Friends, that which is non-knowledge of suffering, non-knowledge of the arising of suffering, non-knowledge of the ceasing of suffering, non-knowledge of the way leading to the ceasing of suffering, this, friends, is called ignorance.
For after all, what is “the way leading to the ceasing of suffering”? It is (the Suttas tell us) the noble eightfold path. And what is the first factor of this path? Right view. Ignorance, then, involves non-knowledge of right view. And right view is knowledge of the arising of suffering; that is to say, knowledge of ignorance. Right view is knowledge of right view, and also knowledge of wrong view, whereas wrong view is non-knowledge of wrong view, and also non-knowledge of right view. And this structure of ignorance is, in fact, Catch-22 at its most fundamental level:
Yathābhūtam na pajānāti: he does not see things as they really are: the phrase — so typical a Sutta description of the puthujjana, the unenlightened commoner — is used here by Heller to illuminate precisely the characteristic of being entrapped in a situation. Not only does the puthujjana have flies in his eyes, he does not see that he has them, and he does not see this because he has them. His dilemma is that though he must find a way to see, yet he cannot find that way precisely because he cannot see. Indeed, he cannot even see for himself that this is his problem. And this is the dilemma which, at its most fundamental level, is the specific concern of the Buddha’s Teaching. The structure of avijjā, the structure of Catch-22, the structure of “having flies in one’s eyes”: they are one and the same. Catch-22 is avijjā. The title character in both the novel and in our lives never appears and yet is omnipresent.
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He also explored the theme of endless repetition in "The Myth of Sisyphus: A Cycle":
“The work is endless!” exclaimed Anuruddha. “No end to the work is apparent. When does the work conclude? When is an end to the work apparent? When will we be able to indulge ourselves carelessly in the pleasures of the five senses?”
“But, dear Anuruddha, the work is indeed endless. No end to the work is apparent. Even when our fathers and grandfathers died the work did not cease.”
“Well then,” decided Anuruddha, “you know about the duties of the household life. I will go forth from home into homelessness.”
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And he wrote a whole book called "Change" which goes into a lot of detail about this topic of recursiveness as found in the Suttas taught by the Buddha. Here is my favourite chapter which approaches the subject with a humorous example:
You and I would have no difficulty in accepting the statement “all circles are round.” It is obvious. Indeed, it is virtually a pleonasm. True, we have not inspected every circle that exists and tested each for roundness. True, we may have personally come across but a minute fraction of all circles that presently exist (let alone those that have been or will come to be). And yet this introduces no jot of doubt into our conviction that all circles are in fact round. Our certainty is structural, not statistical. ...
We saw that experience was hierarchical in its general outlines; we now discover that within experience there exist autonomous hierarchical structures. In the experiential hierarchy “notes — song — concert — evening” the content determined the level within the hierarchy. Notes is more immediate than song and cannot be otherwise. But in the hierarchy of self-deception denial of knowledge is found on every level, and thus describes not a particular level but the hierarchy as a whole. Such hierarchies can be described as replicative, or as recursive.[19]
Recursiveness is important because it offers a stability not present in “ordinary” hierarchies. Remove “an evening on the town” and the entire structure — notes, song, concert — collapses. But remove “denial of knowledge” and we find that…we can’t. Recursiveness is not a feature found merely on each level, like the identical floral pattern on each dish in a stack: rather, recursion is the link between adjacent levels. The denial is always on the next most general level to the knowledge. From the perspective of the knowledge, then, the denial is extra-temporal. As long as we fail to achieve a point of view established outside this hierarchy, knowledge can never escape being encompassed by denial, and the structure must remain inviolable. Thus the structure of self-deception has a stability not found in non-recursive aspects of experience — as everyone knows who has ever succeeded in freeing himself from even the narrowest of such deceptions.
But why go to the trouble of so much self-deception? Why should we be so reluctant to acknowledge the necessity, in experience, of impermanence, when we feel no such hesitation in asserting the necessity, in circles, of roundness? The answer will be found reflected in the entire history of humankind. We seek happiness. We seek freedom. We seek security. Or, more fundamentally, we seek. And so we return, as we must, to craving.
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Bodhesako was writing back in the '80s when computers were just starting and he was aware of some philosophical issues surrounding them:
19. The word might be defined, dictionary style, as: “Recursive: adj. see Recursive.” Curiously, recursive hierarchies seem to play an important role in some branches of Western science, including computer programming, wherein it is essential that such programs do not contain any true recursive hierarchies. For if even one were to be introduced the computer would become involved in an endless cycle and the program would never conclude. In other words, although art may imitate life, a computer program, if it is ever to arrive at a conclusion, had better not do so too closely.
The term “recursive” (as well as several other words) has been adapted with a somewhat altered meaning from Douglas R. Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid (Penguin Books, 1980). Hofstadter’s book is provocative, witty, imaginative, wide-ranging, entertaining, stimulating, and, alas, quite mistaken in its fundamental approach to understanding the human situation. Neither his deterministic views nor (at the other extreme) the free-will views of Prof. J. R. Lucas can come close to the middle way taught by the Buddha.
I think it would be hard to find a better visual demonstration of recursiveness than this (ignore the mathematical formulas at the end if you cannot grasp the abstract concepts -- seeing it is enough):
Mandelbrot set
http://www.youtube.com/watch?v=UuOTuFVnWv0" onclick="window.open(this.href);return false;
Complex non-linear systems:
"These systems are apt analogues for dependent co-arising (paticca-samuppada) in that, despite the fact that their behavior sometimes seems chaotic, their behavior actually contains deep, regular patterns. Furthermore, in some cases, these patterns can be utilized so that the system will behave in a desired way." (Thanissaro Bhikkhu)
http://www.scribd.com/doc/103907285/Shape-of-Suffering" onclick="window.open(this.href);return false;
The dictionary definition of chaos is turmoil, turbulence, primordial abyss, and undesired randomness, but scientists will tell you that chaos is something extremely sensitive to initial conditions. Chaos also refers to the question of whether or not it is possible to make good long-term predictions about how a system will act. A chaotic system can actually develop in a way that appears very smooth and ordered. (Chaos Theory and Fractals)
http://www.tnellen.com/alt/chaos.html" onclick="window.open(this.href);return false;