Saturday, October 13, 2012

Visual illustrations of dependent arising วีดีโอ ปฏิจจสมุปบาท

This video was made to illustrate the Buddha’s teaching on dependent co-arising or dependent origination (paticca-samuppāda) which can be observed at many scales, which means that lessons drawn from observing the world (loka) can be applied to our internal experience of the six senses which makes up ‘our world’. The black hole at the center of a galaxy is like the fundamental ignorance which gives rise to the formations that construct our experience in terms of consciousness being established in name & form. The Buddha compares the ongoing cycle of becoming to the process of planting seeds in fertile soil which is watered by rain.

See The Shape of Suffering by Thanissaro Bhikkhu
‘When there is this, that comes to be; with the arising of this, that arises.
When there is not this, that does not come to be; with the cessation of this, that ceases.
That is, because of ignorance, formations arise. Because of formations, consciousness arises. Because of consciousness, name and form arise. Because of name and form, the sixfold sense base arises. Because of the sixfold sense base, contact arises. Because of contact, feelings arise. Because of feelings, craving arises. Because of craving, clinging arises. Because of clinging, becoming arises. Because of becoming, birth arises. Because of birth old age, sickness, death, sorrow, lamentation, pain, grief and despair arise. Thus arises the complete mass of suffering (dukkha).
‘imasmiṃ sati idaṃ hoti, imassuppādā idaṃ uppajjati, imasmiṃ asati idaṃ na hoti, imassa nirodhā idaṃ nirujjhati, yadidaṃ – avijjāpaccayā saṅkhārā, saṅkhārapaccayā viññāṇaṃ, viññāṇapaccayā nāmarūpaṃ, nāmarūpapaccayā saḷāyatanaṃ, saḷāyatanapaccayā phasso, phassapaccayā vedanā, vedanāpaccayā taṇhā, taṇhāpaccayā upādānaṃ, upādānapaccayā bhavo, bhavapaccayā jāti, jātipaccayā jarāmaraṇaṃ sokaparidevadukkhadomanassūpāyāsā sambhavanti. evametassa kevalassa dukkhakkhandhassa samudayo hoti.’






Or watch another version here:
Avijjāpaccayā sankhārā (Video) | Theravada Dhamma Blog






สรุป ปฏิจจสมุปบาท
ปฏิจจสมุปบาท คือ การที่สิ่งนี้มี สิ่งนี้จึงมี อาศัยกันและกันเกิดขึ้น มี 12 อย่าง ดังนี้
อวิชชา สังขาร วิญญาณ นามรูป สฬายตนะ ผัสสะ เวทนา ตัณหา อุปาทาน ภพ ชาติ ชรามรณะ



เมื่อคิดถึงสิ่งใด แสดงว่าพอใจในสิ่งนั้น

ภิกษุทั้งหลาย !
ถ้าบุคคลย่อมคิดถึงสิ่งใดอยู่ (เจเตติ)
ย่อมดำริถึงสิ่งใดอยู่ (ปกปฺเปติ)
และย่อมมีจิตฝังลงไปในสิ่งใดอยู่ (อนุเสติ)
สิ่งนั้นย่อมเป็นอารมณ์เพื่อการตั้งอยู่แห่งวิญญาณ.
เมื่ออารมณ์ มีอยู่,
ความตั้งขึ้นเฉพาะแห่งวิญญาณ ย่อมมี;
เมื่อวิญญาณนั้น ตั้งขึ้นเฉพาะ เจริญงอกงามแล้ว,
ความเกิดขึ้นแห่งภพใหม่ต่อไป ย่อมมี;
เมื่อความเกิดขึ้นแห่งภพใหม่ต่อไป มี,
ชาติชรามรณะ โสกะปริเทวะทุกขะโทมนัสอุปายาสทั้งหลาย
จึงเกิดขึ้นครบถ้วนต่อไป :
ความเกิดขึ้นพร้อมแห่งกองทุกข์ทั้งสิ้นนี้ ย่อมมี ด้วยอาการอย่างนี้.

นิทาน. สํ. ๑๖/๗๘/๑๔๕.

อิทัปปัจจยตา - หลักธรรมที่เป็นไปตามกฎของธรรมชาติ อันกล่าวถึงกฏเหตุปัจจัยดังนี้ เมื่อเหตุนี้มี ผลนี้จึงมี เพราะเหตุนี้เกิดขึ้น ผลนี้จึงเกิดขึ้น

ปฏิจจสมุปบาทจากพระโอษฐ์





ความจริงไม่มีใครทุกข์ - พระอาจารย์อำนาจ โอภาโส






ความจริงไม่มีใครทุกข์
The Truth is No One is Suffering

พระอาจารย์อำนาจ โอภาโส 

Phra Ajahn Amnat Obhaso

คนส่วนใหญ่ไม่รู้ที่มาของความทุกข์ จึงคิดว่าทุกข์มาจากผู้อื่นกระทำ บางคนก็คิดว่า ทุกข์มาจากเราทำเอง
A lot of people do not know the origin of suffering, therefore they assume that suffering arises from others who did it to them, or else from themselves.

ทุกข์มาจากความไม่รู้ ตามความเป็นจริง
Suffering, stress, pain (dukkha) originates from ignorance, not knowing the truth.

หากเรารู้ว่าชีวิตคืออะไร? เราจะปฏิบัติต่อชีวิตอย่างถูกวิธี
Do we know what life is? How are we going to live life correctly? 

ความจริงในธรรมชาติของจักรวาล มีแค่รูปและนาม เพราะรูปคือมวลสารต่างๆ ที่หมุนรอบตัวเองในที่ว่าง จึงเกิดสนามพลังของนามธรรม อยู่รอบรูปธรรมนั้น สมมุติเรียกว่า คือธรรมชาติแห่งการรับรู้
The truth is the whole universe is only material form (rūpa) and mental phenomena (nāma). Material form (rūpa) is just base matter which spins around itself in emptiness. That which arises around material form (rūpa) is the energy of knowing, the mental phenomena (nāma) that experiences various objects, and this is what we call mind (citta).  

เพราะธาตุต่างๆ ที่รวมตัวอยู่ด้วยกันไม่คงที่ ความรับรู้ที่เกิดขึ้นในช่องว่าง รู้สึกถึงการจะแตกสลาย จึงเกิดความต้องการที่จะเติมเต็ม เกิดความรู้สึกขัดขวาง (โทสะ)
เกิดความไม่รู้ที่แฝงตัวมา 
Due to the fact that these elements are inconstant and the knowing arises in emptiness, they lead to momentary disintegration which conditions the mind to desire things, to go against things, and the ignorance of not knowing what is going on.   
(โมหะ)
เมื่อมันมาก่อตัวกันเข้า เป็นโครงสร้างของรหัสดีเอ็นเอ ที่จะสมานตัวให้ทรงตัวอยู่ได้ จึงพยายามที่จะรักษาสถานภาพนั้น ด้วยการแสวงหาสิ่งที่จะมาเติมเต็ม แก้ปัญหาความพร่องของธาตุสี่ เกิดสภาวะการดิ้นรนของนามธรรม ซึ่งเป็นปัญหาพื้นฐานของสิ่งมีชีวิตทั้งหลายในโลกนี้
When combined together, it becomes structured as DNA, trying to sustain and balance itself within the material form of the Four Great Elements. The mind wants to try to sustain itself and survive, which is the root of the problem for all living beings.
สิ่งทั้งหลายไม่มีอยู่โดยตัวของมันเอง ไม่มีความคงที่อยู่อย่างเดิม แม้แต่ขณะเดียว จึงเป็นสภาวะที่พร้อมจะก่อให้เกิดทุกข์แก่ผู้ไม่รู้เท่าทัน 
Nothing is able to maintain or sustain itself by itself, not even for a moment. Therefore this state will condition pain, suffering, stress to the one who does not understand or know this situation.
สิ่งต่างไม่มีตัวตนด้วยตนเอง อาศัยเหตุปัจจัยเกิดขึ้น (อวิชชา)
Nothing is an individual entity, it depends on causes and conditions (avijjā).

เพราะความไม่รู้ตามความเป็นจริง จึงเกิดความคิดปรุงแต่ง (สังขาร)
Because of not knowing this truth, mental formations arise (sankhāra).

เพราะเกิดความคิดปรุงแต่ง จึงรับรู้ถึงความรู้สึก (วิญญาณ)
Because of mental formations, consciousness (viññāṇa) is conditioned in a certain way.

เพราะการรับรู้ถึงความคิดนั้น จึงส่งผลถึงอารมณ์และบุคลิกภาพ (นามรูป)
Because of consciousness being that way, it influences one’s mental and physical state.

บุคลิกภาพนั้น ส่งต่อให้เครื่องมือการรับรู้ทำงาน (สฬายตนะ)
That mind and body conditions the working of the six sense spheres (saḷāyatana).

เพราะการรับรู้ทำงาน จึงเกิดการกระทบระหว่างภายในภายนอก (ผัสสะ)
The six sense spheres condition contact between the internal and external (phassa).

เพราะการกระทบ จึงทำให้เกิดอารมณ์สุข-ทุกข์ และเฉยๆ (เวทนา)
Contact conditions the feeling of pleasant, unpleasant or neutral (vedanā).

อารมณ์ที่สุขก็อยากได้ อารมณ์ที่ทุกข์ก็อยากผลักไส (ตัณหา)
Pleasant feeling gives rise to desire. Unpleasant feeling gives rise to aversion (taṇhā).

เพราะความอยาก จึงเข้าไปยึดกับสิ่งที่ต้องการ (อุปาทาน) 
Because of wanting, attachment or clinging arises (upādāna).

เพราะยึดกับสิ่งที่ต้องการ จึงลงมือก่อพฤติกรรม (ภพ)
Because of attachment to what one wants, all kinds of actions and becoming (bhava) are determined.
 
เมื่อก่อพฤติกรรมดีหรือเลว จึงเกิดคำว่า “เราดีหรือเลว” ขึ้นในใจ (ชาติ)
Because of becoming either good or bad, therefore the idea of “I am good or bad” arises in the mind (jāti).

แต่สิ่งเหล่านั้นก็เสื่อมสลายไปตามเหตุปัจจัย (ชรา มรณะ)
But everything that has arisen still decays and fades away according to conditions (jarā-maraṇa).

แต่เพราะความไม่รู้ก็หลงปรุงแต่ง แสวงหาสิ่งเหล่านั้น วนเวียนซ้ำแล้วซ้ำเล่า 
Due to not knowing the nature all these things, the process keeps on repeating and regenerating endlessly.
*๑๒ อาการแห่งทุกข์ ที่คนส่วนใหญ่ยังยึดติด ยังหาทางออกไม่พบ และประสบกับปัญหาเพิ่มขึ้น ความไม่เข้าใจเหตุปัจจัย ที่เป็นองค์ประกอบในสายใยของธรรมชาติ 
*These are the twelve links giving rise to suffering that most people are stuck with and cannot find a way out of. They only condition more and more stress due to not understanding the conditions behind these causal links giving rise to suffering, which is the workings of nature.

หากเข้าใจ ปฏิจจสมุปบาท จะไม่สงสัยต่ออดีต ปัจจุบัน อนาคต ว่าเรามีหรือไม่อย่างไร 
เพราะสิ่งต่างๆ อาศัยสิ่งอื่นๆ เกิดขึ้น จึงคงที่อยู่ไม่ได้ เรียกว่า "ทุกขลักษณะ" แต่ไม่มีผู้ทุกข์ (
If there is a true understanding of dependent origination, then doubt won’t arise regarding the past, present or future, whether there is an “I” or not, because everything is conditioned by every other thing, which is also unsustainable and inconstant. This state of inconstancy is called the characteristic of being hard-to-bear (dukkha-lakkha
a), but there is no person who is suffering.   

การเคลื่อนไหวในกระแสของธรรมชาตินั้น มีความสัมพันธ์ส่งผลต่อกันอย่างละเอียดซับซ้อน ด้วยปัจจัยอันหลากหลาย กระทบกระทั่งเชื่อมต่อกันเป็นแพรัศมี สู่ผลอันหลากหลาย
The movement and current of nature in which everything is related is very subtle and intricate. It intertwines with everything else and has different conditioning which results in different shapes and forms in the different dimensions.

"ผลอันหลากหลาย เกิดจากเหตุปัจจัยอันหลากหลาย" พุทธพจน์
“All results arise from the different kinds of causes” according to the teachings of the Buddha.

เมื่อมีสติตามสังเกตการทำงานของกายและใจ จะสามารถใช้เหตุปัจจัยอย่างถูกวิธี 
Whenever there is mindfulness in the investigation of material and mental phenomena, then wisdom will know how to apply these conditions correctly.
เพราะไม่มีใครหนีผัสสะทางอายตนะต่างๆ ได้ เมื่อเกิดการกระทบรู้เท่าทัน ใจก็ปกติ เรียกว่า
Because no one can escape the contact at the six sense spheres, mindfulness knows it immediately. This is called “sīlavisuddhi” - purity of morality.

จิตจึงตั้งมั่นไม่ถูกครอบงำด้วยอกุศลเรียกว่า 
The mind that is steadfast and firm and is unshaken by unwholesomeness, this is called “cittavisuddhi” - purity of mind.

จึงเกิดความเห็นถูกของรูปนามตามความเป็นจริง เรียกว่า
Knowing the true nature of material and mental phenomena the way they really are, this is called “diṭṭhivisuddhi” - purity of view. "
ทิ
และเห็นปัจจัยของรูปและนาม จนหายสงสัย เรียกว่า "
Seeing the conditions and causal relations of mind and body eradicates doubts, this is called “kankhāvitaraṇavisuddhi” - purity through transcending doubts.

สามารถเลือกมุมมองอย่างถูกวิธี ของสิ่งที่เกิดขึ้นกับรูปและนาม เรียกว่า
Being able to view and understand correctly the conditioning process of material and mental phenomena, this is called “maggāmaggañāṇadassanavisuddhi” - purity through knowledge and vision of what is and isn't the way.

เห็นลักษณะความเกิดดับในขันธ์ ๕ ยอมรับความเป็นจริงด้วยใจเป็นกลาง เรียกว่า 
The ability to penetrate the rise and fall of the Five Aggregates and wholeheartedly accept it with a steadfast and balanced mind, this is called “paṭipadāñāṇadassanavisuddhi” - purity through knowledge and vision of the path of progress.

จิตจึงไม่ปนเปื้อนด้วยตัณหาและการหลงคิดปรุงแต่ง ทวนเข้าสู่กระแสธรรมชาติเดิมที่บริสุทธิ์ ซึ่งมีอยู่ก่อนแล้ว คือความสุขหรือพระนิพพาน เรียกว่า "ญาณทัสสนวิส
When the mind is not defiled with craving or mental formations but has entered into “the way things are”, which is peaceful and the origin of all purity, that is the happiness of Nibbāna. This is called “ñāṇadassanavisuddhi” - purity through knowledge and vision.

เพราะสิ่งต่างๆ อาศัยเหตุปัจจัยเกิดขึ้น หากผู้ขาดปัญญาไม่รู้ ก็หลงผิดสร้างเหตุปัจจัยแห่งความทุกข์"
Because everything is conditioned, anyone who does not have wisdom to directly know this, will get lost in these conditions which lead to suffering and stress in their life.
หากผู้มีสติปัญญารู้ จึงเลือกสร้างเหตุปัจจัยแห่งความสุข....
Those who have mindfulness and wisdom will create the conditions for happiness.



บทปฏิจจสมุปบาท ต้นเหตุของทุกข์


Nice chanting in Pali of paticca-samuppāda




Friday, October 5, 2012

Buddhabrot fractals and non-linear chaotic systems


ปปัญจะ  papañca 
กิเลสที่เป็นตัวการทำให้คิดปรุงแต่งยืดเยื้อพิสดาร ทำให้เขวห่างออกไปจากความเป็นจริงที่ง่าย ๆ เปิดเผย ก่อให้เกิดปัญหาต่าง ๆ และขัดขวางไม่ให้เข้าถึงความจริงหรือทำให้ไม่อาจแก้ปัญหาอย่างถูกทางตรงไปตรงมา การขยับขยาย - diversification; diffuseness; spreading; mental diffusion, mental proliferation)


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)

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)





BUDDHABROT FRACTALS

Buddhabrot fractal exploration (based on Mandelbrot set)

Exploration of the 4D mandelbrot set on the Z-plane (Buddhabrot)

Mandelbrot set

Slow deep Mandelbrot zoom

Mandelbrot to Mandelbulb 3D





Fractal Definition: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature.(1)

What is unique about fractals? Many things! But one amazing, characteristic aspect of fractals, is that they are infinite! A fractal is infinite in two distinct senses, the macro level, and the micro level. Fractals extend to infinitely large values of their co-ordinates, outwards in all directions from the center. It would be like starting at the very center of the universe and then moving outward to try and find the end of the universe. Fractals also have infinite detail, in that one can zoom (magnify) in or out without limit (at least in theory) to show ever increasing detail within the image. Another distinguishing feature of fractals is it's property of self-similarity; an arbitrary region of a fractal looks very similar (but not necessarily identical) to the entire fractal. Just as DNA stores all the information that for each of us, all the information for a fractal is contained in its "parent" image. Fractals, in art and nature, can range from beautiful symmetry to the chaotic, from a perfectly symmetrical snowflake to a massive chaotic thunderhead cloud. But regardless of their symmetry, or level of chaos, fractals are everywhere we look and I hope the beauty of fractal art captivates your imagination, as they have mine!





Fractal zoom 2 "The Blue Universe"

Mandelbrot set - from order to chaos
Showing the graph: Occasionally, the plot will become orderly again for a moment, whenever the pink dot passes over a baby Mandelbrot set, but it'll quickly return to the chaotic behaviour. The amazing thing is that, although this chaotic behaviour looks very different from the orderly behaviour, it's created by exactly the same equation, with just a small change to the input value.

A Journey in The Mandelbrot set
This film is based on the exhibition "Seduction" ( http://mandelbrot-set.elica.net/ ) and it blends computer generated images from the Mandelbrot set with digital photographs from the real life. 

2010: A Mandelbrot Odyssey (FractalNet HD)

An epic journey across the Mandelbrot set, exploring many different embedded Julia sets.


Fractal food:  Broccoli Romanesco
Fractal forms—complex shapes which look more or less the same at a wide variety of scale factors, are everywhere in nature. However, some of the most pleasing patterns in geometric art exhibit exact or almost exact self-similarity. These are patterns which are composed of smaller copies of themselves ad infinitum, or at least until some limit where the similarity breaks down due to the granularity of the underlying material.
http://www.fourmilab.ch/images/Romanesco/

Fractal Broccoli.jpg



Mandelbulb
The original Mandelbrot is an amazing object that has captured the public's imagination for 30 years with its cascading patterns and hypnotically colourful detail. It's known as a 'fractal' - a type of shape that yields (sometimes elaborate) detail forever, no matter how far you 'zoom' into it (think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc.).
It's found by following a relatively simple math formula. But in the end, it's still only 2D and flat - there's no depth, shadows, perspective, or light sourcing. What we have featured in this article is a potential 3D version of the same fractal. For the impatient, you can skip to the nice pics, but the below makes an interesting read (with a little math as well for the curious).


Amazing Mandelbulb Gallery with Dhammacakka wheels in a fractal universe:



THE MANDELBROT MONK (who really discovered this? just for fun  ;-)

On a holiday visit to Aachen cathedral, the burial place of Charlemagne, Schipke saw something that amazed him. In a tiny nativity scene illuminating the manuscript of a 13th century carol, O froehliche Weihnacht, he noticed that the Star of Bethlehem looked odd. On examining it in detail, he saw that the gilded image seemed to be a representation of the Mandelbrot set, one of the icons of the computer age. [*3]
O froehliche WeihnachtDiscovered in 1976 by IBM researcher Benoit Mandelbrot, the Mandelbrot set is the most famous fractal (a mathematical object with the property of infinite detail). Only the advent of fast computers made feasible the repeated calculations involved - or so it was thought. [*4] "I was stunned," Schipke says. "It was like finding a picture of Bill Gates in the Dead Sea Scrolls. The colophon [the title page] named the copyist as Udo of Aachen, and I just had to find out more about this guy." The first chapter, Astragali (Dice) was originally thought to be a discourse on the evils of gambling. It turned out to be Udo's research into what we now would call probability theory. He derived simple rules to add and multiply probabilities, and thus devised strategies for several card and dice games. More was to come. In the final and longest chapter, Salus (Salvation), Schipke uncovered the most radical work. Udo had, it seemed, investigated the Mandelbrot set, seven centuries before Mandelbrot.





O froehliche Weihnacht (detail)Initially, Udo's aim was to devise a method for determining who would reach heaven. He assumed each person's soul was composed of independent parts he called "profanus" (profane) and "animi" (spiritual), and represented these parts by a pair of numbers. Then he devised rules for drawing and manipulating these number pairs. In effect, he devised the rules for complex arithmetic, the spiritual and profane parts corresponding to the real and imaginary numbers of modern mathematics. In Salus, Udo describes how he used these numbers: "Each person's soul undergoes trials through each of the threescore years and ten of allotted life, [encompassing?] its own nature and diminished or elevated in stature by others [it] encounters, wavering between good and evil until [it is] either cast into outer darkness or drawn forever to God." Below the description was drawn the first crude plot of the Mandelbrot, which Udo called the "Divinitas" ("Godhead"). He set it out in a 120x120 frame he termed a "columbarium" (i.e. a dovecote, which has a similar grid of niches) and records that it took him nine years to calculate, even with the newly imported technique of ‘algorism', calculation with Arabic numerals rather than abacus. "It tends to be taken for granted," Schipke says, "That the Mandelbrot is too calculation-intensive to be done without computers. What we have to remember is the sheer devotion of the monastic life. This was a labour of faith, and Udo was prepared to work for years. Some slowly-converging pixels must have taken weeks." "But there were also contemporary reasons why Udo's knowledge didn't make it into the mainstream. His basic belief - that salvation and damnation could be determined in advance - was heretical, and his use of Arabic numerals was thought a bit of a black art. And there was the disagreement with Thelonius." Despite the borderline nature of his work, Udo impressed his abbot at the monastery of Sankt Umbertus near Aachen. Life for a 13th century monk wasn't necessarily austere: the scurrilous Cantiones profanae poems record the delights of sex, eating, drinking and gambling. In a footnote to Astragali, Udo writes: "My enumeration of the ways [of dice] helped my lord abbot to win thirty-two florins and a fine new cloak from the Burgermeister at Irrendorf, and he has promised me a helper for my work". But Udo and his helper, Thelonius, ran into instant disagreement. Udo had always interpreted the Mandelbrot as signifying God. Thelonius took the opposite view: that it represented the Devil. Numbers that escaped to infinity, he argued, were souls flying free to heaven, and those caught in an orbit had fallen into the pit of Hell. Like many theological collaborations, they had a schism on their hands. Udo noted that their differences brought all work to a halt, and finally the two were reprimanded by the abbot for coming to blows in the refectory. "Sadly I write," says Udo on the last page of the Codex Udolphus, "that on pain of excommunication I must lay down my dice and my numbers. I have seen into a realm of heavenly complexity, and my heart is heavy that the door is now closed."


Mathematical explanation:


Fractals and math.
In the beginning, God created Math in his/her image. And God said, 'Be fruitful and multiply - and multiply - and multiply...'
Fractals are created using very simple mathematical equations. The fractal I am most interested in is called the Mandelbrot Set and its equation is: z = z * z + c which is about as simple as you get.
These equations are usually referred to as dynamic equations where the output of the equation is fed back into the equation. This is more commonly known as a feedback loop. Nature works very much like this in that it is one big giant feedback loop. For example the leaves from the trees fall to the ground and get fed back into the earth for the next generation of trees and plants. All things in nature work this way, so it's no surprise that mathematical equations using feedback can generate images that look so much like things in nature.
Self-similarity.
Despite its apparent solidity the Universe is a fractal. A fractal is a self-similar pattern or series of patterns with infinite detail. Self-similarity refers to the fact that the patterns repeat themselves within the system but they never repeat exactly. For example, there are many, many galaxies in our Universe but no two are exactly the same. Some look similar to each other (self-similarity) but you could search the whole Universe and definitely not find two with exactly the same details. Our bodies are also self-similar with patterns repeating themselves on different levels. The Chinese and Indian cultures have known this for years, mapping the whole body onto different parts of the body like feet, ears and eyes. Acupuncture and reflexology (to name a few) are based on this theory.
The key is in the details.
The key to the fractal is in the details. You can search the universe of a fractal (each fractal is a universe unto itself since it is infinite) and find the same pattern over and over again but when you look closely at the details you can see that they are quite different. There are over 6 billion people on our planet and again, you will not find two people that are exactly the same. Even identical twins and clones are not exactly the same when you look more closely at the details. It is important to realize this because modern medicine treats everyone as if they are exactly the same instead of realizing that each individual is unique and must be treated differently. The practitioner must take the time to know the patient in all the details before deciding on a treatment for an ailment. This is the biggest mistake of modern medicine.
Fractal dimension.
Another important fact about fractals is that they exist between dimensions. We are use to describing the universe in 2, 3 and even 4 dimensions (including time) but what appears to be solid matter in the universe (galaxies, stars, planets, trees and animals etc�) actually form and exist in the space referred to as the fractal dimension.  Fractal just means �fraction� so a fractal dimension is really just a fractional dimension and would look something like �2.34784� or �3.48723� instead of exactly 2-D or 3-D. Each person has a unique fractal dimension and will respond to different fractal images in different ways.
Fractal healing.
Fractals can be seen in trees, rivers, clouds and all other natural objects. Your own person (body and mind) is a fractal with patterns that repeat on every level of your being. Fractal patterns can be used to restore yourself to the healthy beautiful creature that you really are. A healthy body has all it�s fractal patterns intact on every level, mind, body and soul. An unhealthy body is a body that has had its fractal pattern disrupted in some way causing things to change unexpectedly. You can easily tell a diseased tree from a healthy one because it begins to lose its fractal pattern.
Because of the self-similar nature of fractals, it is possible to work on many levels simultaneously. It has been proven that looking at pictures of nature can increase the healing process dramatically. This is because nature is a fractal. Looking at pictures of fractals has the same effect in generating healing energy and installing the healthy fractal pattern back into the body and soul. The trick is to find the fractal that suits you best. Meditating on a fractal image can be both relaxing and stimulating. The images can trigger the natural fractal properties of our minds and bodies.  It is important to choose a fractal that is pleasing to you since this is more likely to be compatible with your fractal dimension.
What is a Buddhaverse?
A buddhaverse is a universe that is perfected by enlightened beings who realize that they are an itegral part of the universe they live in and that their actions effect how the universe will turn out.  They create the buddhaverse by transforming the ordinary world of desire and suffering into a world of happiness and self-sufficiency through right thought, right action and right livelyhood. In the pure land of the Buddha field, or buddhaverse, beings are in a state of perpetual bliss, where each individual represents a different aspect of Buddha, the embodiment of truth. This pure land or realm of peace and bliss is not a physical place but a living dimension of formless reality intimately resonating with our being. The buddhaverse experience is timeless, perpetually existing, eternally evolving, with no beginning or end.
In Chaos Theory, forms emerge, dissolve, and reform through the creative process known as self-organization. These forms resonate with our spirit and foster a cultivate of connection. Healing originates in the chaotic consciousness and emerges as the process of creative self-organization. Chaos is ubiquitous in nature. It reveals in its own depths, hidden degrees of order and structure that resonate with the soul and reveal to us the basic forms and structures repeated throughout nature and throughout our nature.  It underlies the fundamental laws of nature and natural processes, and implies a universe of evolution and constant re-creation. Structure arises in the moment and is in resonance with its environment. But in a universe of constant evolution each form eventually becomes dissonant as the evolving environment surrounding it changes.
Chaos Theory restores the balance to the entropic forces which lead to the decay and death of outworn systems.  It is the means of creative self-organization which arises from the undifferentiated disorder that lurks within the processes of creation. Chaos holds infinite possibilities of new form, and these forms are eventually revealed and emerge from chaos as new structure. This also applies to consciousness dynamics, such as thought, spontaneous behavior and creativity. Reality is neither structure nor chaos, but a process in which structure and chaos dance between form and formlessness. This is the eternal cycle of death and renewal, the dance of Shiva.
Emergence is a process by which order appears �spontaneously� within a system. When the mind lets go of its rational order and enters into unstructured chaos,  it emerges later with a new structure or form.  Since order arises spontaneously from disorder through self-organization, healing is an ever-present potential.

Wednesday, October 3, 2012

Fractal structure of Borobudur and crop circles in England

Borobudur Temple was built by Modern Mathematical Sciences

A masterpiece of the wonders of the world, turned out beautifully but also built with a powerful intellect as well.


Jakarta, Indonesia – Borobudur Temple was built between the years 750 and 842. But who would have thought the temple was built using a new mathematical calculations known at about the 80’s.
“Borobudur is fractal, a new contemporary geometry structure known in the decade of 80s in the modern mathematical sciences,” said researcher Bandung Fe Institute, Rolan MD, in conversation with AFP on Monday (11/14/2011).

Fractals are geometric shapes that have elements similar to the overall shape. Often a fractal has a certain pattern that repeats with a recursive and iterative.
One of the monumental buildings that have implemented the concept of fractal geometry, according to them is the temple of Borobudur, which is defined as one of the World Heritage Site (world heritage site) by UNESCO.
“The measurements we did on each part of the Borobudur Temple, confirm this mathematically,” says Hokky Situngkir, researcher and president of Bandung Fe Institute, in a recording Videocast that he uploaded on the video site YouTube.
According Hokky, Borobudur was built space that has a similarity with the elements themselves. In the Borobudur, for example, there are many forms of geometry stupa. “Candi Borobudur stupa itself is a giant in which consists of stupas of other smaller ones. Keep up to infinity,” he explains.
In addition, Hokky explains, it is also verified by measurements Parmono Atmadi from UGM, which sees order Borobudur buildings that meet the elements of 9:6:4 ratio.
Ratios, for example, is present at high proportions of three parts of the temple, which is part Arupadhatu (formless world) – the main stupa and stupas that form a circle, the Rupadhatu (the form) – the part that covers stupas are located on the runway square shaped, and the Kamadhatu (lust of the world) – the legs.

Hokky also said, that the actual stupa itself is a form of three-dimensional ellipsoid that satisfy the ratio 9:6:4. “This order we meet in all parts of Borobudur, either horizontally or vertically,” he said.
Not only that, says Hokky, observations of Borobudur Borobudur menyimpulkam that meet the dimensional fractal dimensionality between 2 and 3. “Calculations we find that the dimensionality of the temple of Borobudur is between 2 and 3,” said Hokky via electronic mail to VIVAnews.
Read more: http://scienceray.com/mathematics/borobudur-temple-was-built-by-modern-mathematical-sciences-2/#ixzz283mUHijx



About the mathematical structure of Borobudur see this article:

The Sacred Geometry of Perfect Forms in East and West
Identical Geometric Forms - The square, the circle, and the triangle 





Compare with this:

Crop Circles: A Perspective From the Ground Up

After years of studying sacred geometry—the mathematical geometrical structures inherent in all life forms—I realized that crop circles are predominantly based on the same principles. Knowing from experience how hard it is to draw the most basic of the geometries by hand, even using a compass and a rule, I realized that the complexity and intricacy, the sheer size of these formations is such that only a higher intelligence could create so detailed an image that can only be truly appreciated from an aircraft. Tony agreed that only a higher intelligence could be capable of creating such complex and mathematically perfect design structures. We discussed how we both know people who are experts in computer graphics and admit that even they find it difficult to replicate the designs, which would require many many hours and calculations.


The area of southern England where Chithurst Buddhist Monastery is located has some interesting natural features and also a spiritual history. There are Iron Age remains from the Celts who used to live here and worship trees, and then from the Romans who came after them and built roads and towns. One unusual thing that happens here more than anywhere else are the crop circles which appear very quickly overnight in the fields and nobody could explain how it is possible. Some of the recent ones from Wiltshire (near Stonehenge):





During the big floods in Thailand in 2011, the Buddhist park at Nakhon Pathom called "Buddhamonthon" offered a spectacular view from above:

Buddha-mandala
พุทธมณฑล







"Whatever form is past, future, or present; internal or external; blatant or subtle; common or sublime; far or near: that is called the aggregate of form (rupa-khandha)."