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A 21 st century scientific perspective on Buddhism 

By Minh-Khong 

© Copyright 2011. All commercial rights reserved. Any reproduction in whole or part, in any form, for sale, profit or 
material gain is strictly prohibited. The reprinting of this in its entirety, for free, unconditioned distribution is allowed after 
prior notification to the author - minhkhongOOO at gmail dot com . 


2500 years ago, things were simple, life was simple, and science was in an infant stage. 
Today, things are complicated, life is complicated, and science has advanced so much that reading 
Buddha's teachings about emptiness nature of all phenomena is incomprehensible to most people. 
Buddha's teachings were adapted to the understanding of the people at the time, using the language 
and knowledge of people at the time. Those don't seem to suit people's scientific quest for knowledge 
nowadays anymore. People don't believe unless things are explained in a scientific way, especially 
those with higher education. 

This paper is an attempt to use today's science methodology to convey, in 21 st century terms, 
Buddha's teachings especially on emptiness nature of all phenomena. Scientific model using fractal 
transformation for the law of universal causation commonly known as karma is introduced to explain 
rebirth, Buddhist's six realms of existence, enlightenment concepts and the emptiness nature of all 


Today's science has advanced so much that scientists take on the roles of authorities 
regarding the objective, physical world [1]. However, when it comes to our minds, little is known. 
Scientists are troubled on how to character or analyze the mind (consciousness) using similar 
methodologies as they have done with the physical world. Cognitive and behavior sciences have 
emerged but can not explain consciousness, experiences of growing numbers of people reporting 
"experience after death" or the state of the minds of monks in deep meditation. 

Growing numbers of conferences, symposiums and dialogs [2] between scientists and 
Buddhist monks have happened to bridge the gap between scientific methodologies in materialistic 
science and Buddhist methodologies in mind cultivating. 

However, the differences between scientist's and Buddhist's approaches are deep rooted from 
the very foundation of science and Buddhism. This paper examines the foundations of science and 
Buddhism and proposes a scientific model to represent Buddhism theology. 

"Buddhism and Science: Confrontation and collaboration", presented at International Conference on "Buddhism and Science" 
Central Institute of Higher Tibetan Studies, Sarnath, Varanasi by Dr. B. Alan Wallace 

http://www.newdualism.Org/papers/B. A. Wallace/Wallace-Buddhism%20and%20Science-2008.pdf 
2 nd Buddhism & Science symposium, July 15, 2010 in Singapore. 
The 3rd World Conference on Buddhism and Science, December 1-2, 2010 in Thailand 

Buddhism and Science: Cross road of the future, December 4-5, 2010 at Maitripa College, Portland, Oregan, USA. 
The dialogs between HH Dalai Lama and quantum physicists - 
The dialogs between university researchers and the HH Dalai Lama- AGhAP7pzc&feature=relmfu 

Foundation for science: 

In science, according the Oxford dictionaries a postulate is "a thing suggested or assumed as 
true as the basis for reasoning" [3]. Therefore, a postulate is a proposition that is not proven or 
demonstrated but considered to be self-evident. Once you've accepted the postulate, other rules or 
laws can be deduced from these basic "foundation" and the whole science on this is formed. 

For example, in Euclidian geometry, the first postulate [4] is that "you can only draw one 
straight which is also the shortest line between two points". Another postulate is that "you can have 
one and only one plane containing any 3 arbitrary points in space". These are fairly "obvious" to 
accept. This is the "Euclidian geometry" that we know and it is used in every day's life to build 
geometry shapes as our house, table, chairs. 

On the other hand, in the theory of relativity, Einstein's postulate [5] is that "light is always 
propagated in empty space with a definite velocity c which is independent of the state of motion of the 
emitting body". This is a little bit harder to be "obvious" that is if you travel at the speed of light, you 
still perceive light traveling at that same speed c which is approximately 300,000 kilometers per 
second. This is as opposed to if you travel on a car at 60 miles per hour, you would see other cars 
traveling along at same speed as if they were stationary. However, since the rules deduced from this 
postulate are able to explain phenomena observed with stellar movements and the famous E=M*C 2 
equation deduced from this rule agrees in phenomena observed in atomic phenomena, this is 
accepted by scientists. 

Next to postulates is a set of basic rules or laws that can not be proven but observed to be 
true. For example, in Newton's dynamic mechanics, the 2 nd law [6] states that the acceleration of an 
object asserted by an external force is proportional to the force and inversely proportional to the mass 
of the object (a = f/m or f = m*a). This law is observed by experiments but can not be proven (via 
mathematical means). Things around us - cars, machinery - are the results of applying this law. 

All other laws can be proven, deduced from the postulates and those basic rules to become a 
science. Any theory, phenomenon that doesn't conform to those "science laws" is deemed to be not 

People used to think science is absolute, is truth. In fact, science is only relative truth, 
"perceived truth". The postulates are formulated via empirical experiments or observations. The 
formula is then "generalized" to include all objects. Once a phenomenon is discovered that violates 
the postulate, another postulate is formed to cover the case and a "new" science is formed. 

In science history, the Newtonian physics can not explain the observed movement of stellar 
bodies or atoms. Einstein's theory of relativity is able to explain that and becomes a super-set of 
Newtonian physics. Einstein's relativity physics can not explain today's observation of sub-particle 
behavior. Quantum physics is realized to explain those. 

3. Oxford's definition of "postulate" - 

4. Euclidian geometry postulates -, articleld-18770.html 

5. Einstein's theory of relativity postulates - 

6. Newton's dynamic mechanics laws - 


Foundation for Buddhism: 

With Buddhism, to be seen as a scientific model, it is proposed that the first postulate is that 
"all sentient beings have the same nature and this nature is basically emptiness". This is much harder 
to accept as "obvious", most would accept this via their belief instead. 

Next is a set of rules on dependent-arising phenomena [7], namely 






th Ignorance as condition, Mental Formations arise 

th Mental Formations as condition, Consciousness arises 

th Consciousness as condition, Name and Form arise 

th Name & Form as condition, Sense Gates arise 

th Sense Gates as condition, Contact arises 

th Contact as condition, Feeling arises 

th Feeling as condition, Craving arises 

th Craving as condition, Clinging arises 

th Clinging as condition, Becoming arises 

th Becoming as a condition, Birth arises 

th Birth as condition, Aging and Dying arise 

These are so important in Buddha teachings that Buddha himself said "Deep is this dependent 
co-arising, and deep its appearance. It's because of not understanding and not penetrating this 
Dharma that this generation is like a tangled skein, a knotted ball of string, like matted rushes and 
reeds, and does not go beyond transmigration, beyond the planes of deprivation, woe, and bad 
destinations" [8]. 

Last is the laws of karma i.e. "cause and consequences" of good/bad actions/behavior as the 
seed for subsequent actions or behavior (analogous to the "force" in Newton's 2 nd rule of mechanics 
sense). These are disclosed in very detailed in the Patthana section of the Abhidhamma [9]. 

Only when you fully accept the postulate, dependent-arising rules and karma laws, then the 
rest of Buddha teachings would make sense. Otherwise, there would be areas where doubts arise 
since they don't have a solid foundation to base on. 

On 12 links of dependent arising - 

Transcendental Dependent Arising, A Translation and Exposition of the Upanisa Sutta by Bhikkhu Bodhi 

Maha-nidana Sutta - http://www.accesstoinsiqht.Org/tipitaka/dn/dn.15.0.than.html 

The conditionality of Life - 

Scientific model for Buddhism: 

In science, there is a mathematical field called fractals or cellular automation [see appendix]. 

Since fractal patterns are observed in nature and material-like shapes can be composed using 
fractal transformation, it is suggested that fractal transformation can be used to model the karma 
causal effect in Buddhism. However, in mathematical fractal transformations, the formula for the 
transformation is fixed from cycle to cycle. In this model, it is generalized so that transformation 
changes from cycle to cycle using dependent-arising rules and karma laws as described earlier in the 
foundation of Buddhism section. But since karma composes of common (collective) karma and 
individual karma, the transformation formula is "similar" for the most part for the collective karma but 
with minor "variants" for the individual karma. This is similar to where DNA of siblings is similar for the 
most part but there are minor variations between them. In analogy to fractal decompression process 
of images, one can achieve any form or formless material or beings after eons of the karma fractal 
transformations from a uniform "emptiness" as a starting point. 

This is our scientific model of the progress of this world, our lives, and science. Each stage of 
mental or scientific development corresponds to a fractal detail level. But unfortunately karma so far 
can only be described qualitatively. It is a challenge to quantify karma using scientific tools. 

We went from the "4 basic materials" - earth, water, fire, wind - to describe things we know to 
a molecule level than to atomic level, sub-atomic and now quantum level. It is not surprising that as 
we progress, science will keep finding more details, the never ending fractal details. This model 
explains the materialistic view of science, a perceived reality (toward more fractal details) and 
Buddhism mind purifying process (toward less fractal details). This model explains our lives, our 
thoughts, as time progresses, we'll get more "sophisticated", more "detailed", more "materialistic" but 
farther away from our basic "true nature", the root of all things. 

Science is moving into the "more detailed" direction whereas Buddha teachings are trying to 
get us to go to in "coarser level" direction i.e. severing the dependent arising cycles and unwinding 
the fractal cycles so that ultimately we would get closer to our "true nature" - the root, the 

Recently the Dalai Lama offers science community to probe/measure brain waves of highly 
trained monks in meditation [10]. No doubt they will find explanations in science terms the meditation 
process and why the stages of meditation or state of the minds progresses in such way. They would 
be all true, at "that scale" in the "fractal structure". These details are more "materialistic", "perceived 
details" and are farther away from the "real truth", the "true nature of things". 

10. Scans of Monks' Brains Show Meditation Alters Structure, Functioning - Alters Brain WSJ ll-04.htm 

Now, the Venn diagram [11] can be used to describe the relationship of Buddhism's view and 
scientific views - Buddhism postulate, dependent arising rules and karma laws are denoted as the 
heavy circumference, all dharmas as the result are indicated as the grey area inside. Smaller circles 
indicate various science postulates and their internal grey areas are the resulted associated sciences 
- math, geometry, calculus, physics .... 

Other ^"^^^^^ Buddhism 

Buddha f x^ y^ postulates 


X \ / \ 







Sciences that don't see the same view as that of Buddhism are likely operating under a 
different set of "global" postulates as indicated in the dotted line and its internal area. 

From this, we can see that there are areas that are common and we all can agree and there is 
area where there are differences. It all depends on the "original postulates" that we base on whether 
they are the same or not. So, in arguing on a subject whether it is right or wrong, it is important to 
see whether the implied assumptions are the same. Today's science is still searching for the "global" 
postulates such as the big-bang theory to explain the existence of this world (note that the big-bang 
theory is not absolute truth, it is as valid as its postulates assume). Various sciences today are in 
agreement with Buddhism as in the diagram above especially quantum physics in the emptiness 
nature of particles and interactions among objects. Those sciences that are in agreement with 
Buddhism are put inside the "Buddhism circle". For example, various "science circles" are within the 
"saha world circle" which is the world we perceive and live in today. The global postulate circle, the 
big bang theory for example, encloses the saha world circle. Note that all sciences to date have 2 
common postulates - space and time. The Buddhism postulates and dependent arising rules would 
lead to space and time concept (as explained in page 7 below). That's why "science circles" are 
enclosed by "Buddhism postulate circle". This diagram can also explain the existence of countless 
other existing Buddha worlds, Amitabha for example, besides our saha world. 

11. Venn diagram - diagram 

Traditional "emptiness" [12] in Buddha's teachings can be interpreted in this scientific model 
context. In the past, there have been discussions as what this "emptiness" really means [13]. From 
the Venn diagram above, you can see that since the "Buddhism circle" is outside the "our saha world 
circle", there are phenomena that are beyond the grasp of our world and its science which are limited 
in knowledge via the "established postulates" at the time. As the result, at the time of Buddha 
teachings, there wasn't any other proper word other than the word "emptiness" to explain the true 
nature of sentient beings. While this true nature itself is unchanged, but to better describe this true 
nature in today's terms i.e. within the bounds of today's science postulates, "pure energy life form" 
would be more appropriate to represent our true nature. While this still can't convey the true nature of 
"emptiness" (as it would be comprehended by Buddha or any enlightened being), it would be "closer" 
than just "emptiness" since the science at the time of Buddha teachings, people knowledge was much 
more limited than what we have today. 

This is similar to as using a circle in 2-dimensional geometry to describe a sphere in 3- 
dimensional space. Expressing this using Diamond sutra style - "the circle we are referring to is 
neither circle nor not circle, it is not really such, it is just called by that name" i.e. the circle is not really 
circle since it's just a name to describe the sphere which is inconceivable in 2-dimensional terms. 

This is an analogy to a similar verse in the Diamond sutra - "And Buddha answered: Subhuti, 
those to whom you refer are neither living beings nor not-living beings. Wherefore? Because "living 
beings", Subhuti, these "living beings" are not really such; they are just called by that name." [14] 

Why is "emptiness" being energy ? First refer back to the Heart sutra: 

"The characteristics of the voidness of all dharma are non-arising, non-ceasing, non-defiled, 
non-pure, non-increasing, non-decreasing" [15] 

In today's words, this refers to the "law of conservation of energy" - energy can not be created 
nor destroyed (non-arising, non-ceasing). Second, this also refers to, according to the 2 nd law of 
thermodynamics, an energy body in perfect equilibrium where its entropy [16] is at maximum i.e. 
perfectly uniformed (non-defiled, non-pure, non-increasing, non-decreasing). 

12. On Buddhism emptiness - 
Emptiness - Cula-suhhata Sutta 

13. The Essence of Other-Emptiness, by Taranatha, translated and annotated by Jeffrey Hopkins 
Snow Lion Publications, 2007 

14. Diamond Cutter Sutra (vajra prajna paramita sutra) Published by the DaeJang Gyong Research Institute of Haein-sa Monastery, 
Korea, p-12. 

15. Prajna Paramita Heart sutra by translated by Tripitaka Master Hsuan Tsang, commentary by Grand Master T'an Hsu , 
English translation by Ven. Master Lok. 

16. Entropy is an indication or measurement of how well a "system" is distributed uniformly. For example, a glass of water and ice 
would have smaller entropy than that when the ice is melted (more uniformed). The 2 nd rule of themo-dynamics states that for an 
isolated system, the entropy of the system can only be the same or increasing i.e. can not decrease. For example, a drop of ink in 
a glass of water would tend to spread to get the ink dissolved evenly in the water i.e. more uniformed. Any machine, device such 
as "perpetual motor" that would decrease the entropy of an isolated system is scientifically impossible. 

If applying Einstein's famous equation E=M*C 2 that describes the transformation between 
energy and matter, one can easily see why in the Heart sutra - "All things are marked by emptiness" 
where "emptiness" is energy as the interpretation above. Note also that energy in its pure form has 
never realized in today's science. We always perceive energy in forms like heat, light, electricity, 
gravity, motions, chemical bonds ... 

This "energy body" is not similar as "passive" energy we know in today's science but this 
energy body is a "life form with ultimate wisdom". Keep in mind that this is the "perceived emptiness" 
within the bounds of current science, the mapping of "true emptiness" into today's "scientific systems". 

Now, starting from "emptiness", if for some reason, this "emptiness" is "shifted" i.e. not in 
perfect distribution state any more, "ignorance" i.e. not knowing the truth would result in a "mental 
formation" that there is some part of this "emptiness" is "different" than "other part" of this emptiness. 
The consciousness of "self" and "non-self" is formed (and also the consciousness of space). Once the 
consciousness of "self" and "non-self" is formed, there would be a consciousness of the "boundary" of 
the "self" and the "non-self" i.e. form is realized. Once the "form" is realized, at this boundary, there 
would develop a "sense" consciousness to be able to "feel" the other side and eventually a sense 
organ is formed (consciousness of changes leads to consciousness of time). If the rules of 
dependent-arising and karma keep applied, it would end up with the first simplest "living beings" 
whether they are viruses or micro-organisms. Imagine the rules of karma and these fractal dependent 
arising cycles keep going for eons, what we have is our world, our societies, our science as we know 
today. Note also that this example doesn't imply the "first cause" i.e. how this universe if formed. The 
explanation is still within the bound of today's science to clarify the 12 dependent-arising phenomena. 

Fractal transformation has been used for image compression. In fractal image de-compression 
[17], one starts from a uniform gray sheet and the fractal decompression formula is applied over and 
over to restore original object. Similarly, one can start from pure uniformed energy to end up with a 
real objects or beings after eons of fractal transformations of dependent arising cycles and karma 

-> Fractal de-compression -> 

On the other hand, if all materials in this universe transform into pure energy and the energy is 
distributed perfectly evenly i.e. at maximum entropy state, it would become "one", "no-self" because 
of the uniformness; no part could be differentiated from "other part". The time concept would cease 
since the state of this uniform energy stays unchanged, there is nothing to "mark" the past, present or 
future. Space concept would also cease since there is nothing to mark "here" and "there". Keep in 
mind that this interpretation is still bound by the limit of today's science. As science progresses in the 
future, the science's postulates are "enlarged" to be a superset of today's science, the "perceived 
emptiness" and "fractal transformation of karma laws" would (or should) be then re-modeled to be 
closer to the "real truth". 

17. Fractal image compression, AK Peters, Ltd. by Michael F. Barnsley & Lyman P. Hurd 
Fractal decompression sample - projects/image processinq/web/FractallmaqeCompression 

To further verify this fractal model against Buddha's teachings, from the Diamond sutra: 

"Yet when vast, uncountable, immeasurable numbers of beings have thus been liberated, 
verily no being has been liberated" [18] 

That can be visualized symbolically as described by a fractal structure below. If each sentient 
being is represented as a "detail" on a Von Kock fractal structure [19]. When a bodhisattva helps to 
liberate many sentient beings as symbolically depicted in the heavy line below, none was liberated 
(sentient beings that were liberated are all the detail levels from that heavy line if the fractal 
transformation were applied from that level). 

Through this, we can see that when all sentient beings are "liberated" (i.e. getting to the "root"), 
"no sentient being was liberated" and the end result is a unified "one", "no-self", the "emptiness". 

This example is fairly simplistic to convey the idea. The actual dependent-arising rules 
according to the karma of each sentient being and the complex network of inter-karma of beings, 
when applied, sentient beings would move toward or away from the "root" depends on their good/bad 
karma in the past (lives). The world would move away or toward the root also depends on the 
collective karma [20]. The quantum physics view of interaction among particles or objects is very 
similar to this inter-karma among sentient beings. 

18. Diamond Cutter Sutra, published by the DaeJang Gyong Research Institute of Haein-sa Monastery, Korea, p-1. 

19. Fractal Von Kock's curve - 

20. Cakkavattisihanada Sutta - D=29 

In Buddhism, sentient beings are born according to past karma into each of the 6 basic 
realms- god, demi-god (asuras), human, animal, hungry ghosts or hell realms [21]. 

The picture below is to symbolically depict how the 6 realms of existence in Buddhism are 
perceived from this scientific model. 

At the center core is our "Buddha nature". 
The 1st cylinder layer is the god realm where their karma is "very light". 
The 2 nd cylinder layer is the demi-god realm where their karma is "thicker" then that of the god realm. 


The 3 cylinder layer is the human realm 


The 4 cylinder is the animal realm where their karma is worse than that of human's. 
The 5 th cylinder is the hungry ghost realm where their karma is worse than that of animal's. 
The 6 th cylinder is the hell realm where their karma is worst. 

Buddha nature 

God realm 

Demi-god realm 
Human realm 
Animal realm 

Hungry ghost realm 
Hell realm 


21. Six realms of existence in Buddhism - 

The karma can be visualized as a cloud covering and hindering our Buddha nature to see 
things the way they really are. This "karma shield" causes us to perceive things (including our present 
forms) according to the realms we are in whether we are a god, a human or an animal ... The "thicker 
the shield", the "farther" we are from our true nature. We perceive life starting and ending as this 
karma shield changes its state according to our past karma. That's how we "die" from one realm and 
"reborn" to the other realm or reborn in the same realm. When one reaches enlightenment, all these 
"karma shields" are shredded, one returns to his/her true nature. 

This gives insight to the re-birth process that most westerners find it's hard to believe. 

Buddha taught various dharmmas according to the past karma of each person. Therefore, 
there are recorded teachings in various levels. Unfortunately, that makes it difficult for us to know 
where to start and where to go next. The best is to try everything first, once you see a pattern on a 
particular sutra or methods easy to understand or feel more "suitable" to you. Then try to go deeper in 
to that line of sutras or method in more depth and details. 

Various dharma practices such as zen, chanting, pure-land and tantras are methods to 
effectively sever the dependent-arising cycle. This effectively opens a "channel" through these "karma 
shields" to gain access to our Buddha nature. That is why when this channel is open, people often 
feel a vast tranquility upon reaching Samadhi state (concentration or absorption state of mind). This 
access allows us to "see" things "better", to understand the "Buddha teachings" better via our own 
Buddha nature. Doing it frequently, it's like a "boot-strap" process with positive feedback. It makes it 
easier "next time" we try to open this channel again since we are "wiser", we understand Buddha 
teachings better which in turn helps the next time. People meditating, who frequently open this 
"channel", can keep the duration of the channel longer and/or "widen" channel. This explains why 
some sages have gained the "god/divine eye" ("eye" that can see through material objects, can see 
sentient beings in other existence), the "wisdom eye" ("eye" that can see the true nature of things) 
and/or the "dharma eye" ("eye" that understands all dharmas, can see karma in the past and lives in 
the future as the result of past karma) as they are able to easily access their Buddha nature that has 
the ultimate wisdom [In contrast, today's science can not predict exactly an outcome of throwing a 
dice since all the factors affecting its movement are too numerous to be accounted for. Only a few 
primary factors are included within computing power means to calculate the probability of the dice 
landing position]. 

That's why (be able to access to the Buddha nature) Nagarjuna was able to comprehend the 
"real emptiness" in his analysis of emptiness [22]. That's why Vimalakirti comprehends the 
"inconceivable liberation" ability of Bodhisattvas [23]. Describing these using the words at the time are 
mostly difficult to comprehend and are often being disregarded by today's science. 

If the positive feedback is strong enough, it causes an avalanche effect and all the "karma 
shields" are shredded, one achieves enlightenment. 

When a person dies or has near-death experience, there is a brief moment he/she has access 
to the Buddha nature when the "karma shield" is transformed. This explains how they could see their 
past lives and karma. For experienced dharma practitioner, this gives him/her an opportunity to 
escape the birth/death cycle [24]. 

22. Causality & emptiness, The Wisdom of Nagarjuna - file/naqarjuna.pdf 

23. Vimalakirti Nirdesa Sutra - 06.html 

24. About Bardo - http://buddhism.about.eom/od/vairayanabuddhism/a/bardothodol.htm 



The foundation of Buddhism has been analyzed using scientific approach of postulates and 
basic laws. Venn diagram has been used to represent the Buddha dharma in relation with other 
sciences. Fractal transformation has also been used coupled with those postulate and karma laws to 
represent the form and formless formation of materials and sentient beings as seen in Buddhism 
theology. It also gives insight to rebirth concept, the Buddhist's six realms of existence as well as 
enlightenment concept. This scientific model is also verified against traditional Buddhist scriptures. 

We hope that these would give those with scientific mind a good solid foundation to spark their 
belief in Buddhism and those who are already on the path something to re-assure their belief in this 
scientific world. In reality, this world and our perceptions seem very real to us, we have to deal with 
them the best we can to reduce our bad karma. In practice, just like science, one doesn't dwell into 
details of the basic formulas for quantum physics or classical Newtonian physics to believe in every 
day's phenomenon as how a car, a boat or a space vehicle works. In Buddhism, one would use the 8- 
fold path as the general compass to make sure the direction taken is, in general, correct. The 
teachings, stories, advises in the Tripitaka as well as analysis, explanations by dharma masters 
would provide more details and examples suited to each person's level, depending on where he/she 
is on "the path". 

To conclude, "If there is any religion that would cope with modern scientific needs it would be 
Buddhism" which is believed to be a quote from Einstein. 


Appendix - Fractals 

In fractals, if the same rule, formula, or algorithm is applied over and over again, it results in an 
interesting outcome. For example, if the "rule" is to make a "mountain" in a middle of the line segment 
(Von Kock curve [19]) 

Now apply the same rule on the new line segments 

If this rule is applied over and over again, the figure would tend to "converge" to some shape 


called "conjecture" of this "rule". Here is the 5 order Von Kock curve 


These fractals have been recognized in natural shapes [25], for example a "fractal fern". 

Another example is Romanesco (a cross between broccoli and Cauliflower, which accentuates 
the great fractal spiral patterns on the top) 

25. Fractal in nature and synthetic fractal - math patterns/visual-math-natural-fractals. html 


Or it could be totally synthesized with pure mathematic equations as in this Iterative Desert 
Landscape: this windswept landscape, looking a bit like sandstone is completely generated by 
math/fractal equations 

DNA structure and its passing from parents to children is another example of a fairly 
complicated iterative structure in nature. 


An amazing characteristic of fractals is that at any "coarser" level, one can always go to a 
deeper "detailed" level and find more details which is often referred as "artificial details" as in the well 
known Mandelbrot set [26]. 

Excerpts from 

The Mandelbrot set shows more intricate detail the closer one looks or magnifies the image, usually 
called "zooming in". The following example of an image sequence zooming to a selected c value gives an 
impression of the infinite richness of different geometrical structures, and explains some of their typical rules. 

The magnification of the last image relative to the first one is about 10,000,000,000 to 1. Relating to an 
ordinary monitor, it represents a section of a Mandelbrot set with a diameter of 4 million kilometers. Its border 
would show an inconceivable number of different fractal structures. 



Step 2 

Step 3 


Step 4 

Step 5 

Step 6 

Step 7 

Step 8 

Step 9 

Step 10 

Step 11 

Step 12 

Step 13 

Step 14 

26. Mandelbrot fractal and artificial details - http://en.wikipedia.orq/wiki/Mandelbrot set