RENSSELAER POLYTECHNIC INSTITUTE
The Tree of Life
Fractals at work subconsciously
Kosta Andoni
3/27/2014
All organisms are a product of their environment. While human civilization has
developed to be superior over other aspects of nature, humans continue to have a conscious
understanding of the world around us. When we’re hungry, we locate food and consume it.
When we are tired, cold, or hot, we seek shelter. Today, many of these aspects of survival are
taken for granted by a majority of human societies as a result of continuous advancement in
technology and culture. Let’s backtrack to the beginning of the homo homo sapiens race. Here
we see a few primal humans traversing their native lands following the herds and the seasons,
still a part of the flow of nature. We can follow the evolution of human society from that point
to today and the progression will be coherent. The nomads began to farm and agriculture
allowed for a technological advancement through the years. One thing led to another and the
human race conquered the world. The question is why does humanity function the way it does
today? The answer comes from nature. Subconsciously, humans are a device of their fractal
environment which is exhibited by their culture in political, religious, and social aspects.
In ancient mythologies and religious writings, there is a reoccurring motif called the
Tree of Life. In many contexts, a tree is revered as the source of life or sometimes as an
intersection between the plane of the life and the plane of death. Contemporarily, we can
confirm that trees don’t possess this sort of fabled mythological power but the creators of these
myths surely believed in it. The most amazing part about the “tree of life” is that it appears to
be a universal constant in various mythologies, religions, and philosophies over extended
periods of time in all regions of the world. In ancient Persia, the tree was large and sacred and
bore all the seeds of life. In ancient Egypt, the acacia tree stood on the boundary between the
world of the mortal and the afterlife. In the Catholic faith, the tree of life represented a pure
state of humanity. In Islam, the Garden of Eden was only one tree, the tree of life. In Judaism,
the tree forms the interconnections of the nodes of the Kabbalah. 1 Accounts of a tree of life go
on and on for millennia and appear in so many diverse extensions that it becomes very unlikely
to be a coincidence. In many cases, the tree of life is a symbol of the entire world branching off
from one origin. And don’t forget Yggdrasil in Norse myths.
To understand the connections between the world we live in and the tree of life or any
tree for that matter, we must first explore the geometry of fractals. A fractal is characterized by
the repetition of similar patterns on ever-diminishing scales.2 From this definition, it is clear
that a tree is fractal. The trunk splits into branches and those branches become the new trunk.
The branches then split off into smaller branches and the process repeats recursively
indefinitely. If the tree were a true fractal, the recursion would continue forever as the limit
approaches infinity. However, the earth is finite and the recursion of the tree must follow the
limits of physical space. To account for this quasi-fractal property in this example and
subsequent ones in this paper, the word fractalesque will be used. Because written record isn’t
the most complete over the course of history, only assumptions can be made as to why so
many human civilizations and cultures share this widespread component in their spiritual
attachments. The most reasonable assumption to make is that this myth arose from the
observation of nature. Whether this decision was a conscious or subconscious one to its
owners, human civilizations still subconsciously follow the branching of the tree of life.
How are we trees? As humans, we ourselves are not trees but a solid case can be made
for many structures around us both physical and abstract. To incite the insight, the best place
to start is the beginning of civilizations. While nomads had some aspects of community and
culture in their lives, not enough proof of this interconnectivity as a society is evident for the
hunter gatherers. Anthropologists have concluded that hunter gatherers did form in small
egalitarian group where everyone had equal influence.3 This fact helps lay down a contrast for
our current social structure. The beginning of current society started with the Agricultural
Revolution where peoples began to settle in fertile river basins where they could cultivate crops
and domesticate livestock in order to survive. These original communities planted the seed for
the tree the fractalesque societies we have now. In regards to social standing, much of the
social experience of the human race has been a non-egalitarian structure unlike the nomads.
Here the tree of life begins to emerge. Generally speaking for many societies since the
Agricultural Revolution, there has been a single ruler with dictatorial powers over all and is
therefore the trunk of the tree. The dictator cannot run the entire realm by him/herself so they
appoint a cabinet of advisors or a council or a court or ministers to assist which significantly
begins the branching off from the tree trunk. The cabinet then branches off to be responsible
for the wealthy upper class. The same occurs from upper class to middle class and once again
more branching to encompass the lower class or slaves. Slavery creates a more understandable
effect because the upper and middle classes did possess these human lives under their
command. Regardless of the specifics, we see a branching out of power in society that follows
1/f noise. The less frequent aspect, the ruler, has more power than the more frequently
occurring. A good example of this fractalesque social breakdown is the feudal system
incorporated during the Medieval Era. In feudalism, the king would be the trunk and then
dissipate his power to the lords/nobles who then appointed their knights with responsibility
who were in turn in command of their peasantry. 4
Figure 1: Branching of power and responsibility in the feudal system 5
To contrast the abstract fractalesque representation of social hierarchy, physical
geographic representations can be considered. At the beginning of civilization, ancient settlers
settled at fertile river deltas such as the Nile (Egyptians), Euphrates and Tigris
(Mesopotamians), and Indus (Indians). Their judgment in carving civilizations in these areas is
easily justifiable. In order to survive, the river civilizations grew crops in proximity to rivers that
constantly flooded to deposit fertile sediments in the soil.6 To accommodate for the need of
drinking water and crop water when the rivers weren’t flooded, these river civilizations would
implement intricate irrigation techniques that branched from the field to the river and its
tributaries to provide a source of water. Fractals come into play here again. If we treat the river
as the tree trunk and its tributaries as its branches, the irrigation system completes the fractal
model by further branching it out into the field. Along the way, each water path scales down in
size further supporting fractalesque tendencies and observations in these societies. The idea
that rivers are fractals has been brought up before and is recognized by many. 7 It wouldn’t be
that much of a stretch to claim that early civilizations noticed this fractal pattern and exploited
it for their benefit. This theory of civilization resource-grabbing can be applied to any resource
of importance to a society. Civilizations tend to branch out paths to these resources and the
easiest path is well-traveled over time. A current day example of this in the United States is the
Interstate Highway System. A traveller is more likely to use the highway on a long trip rather
than the back roads to save time and energy.
The branching out pattern of society leads to towns and cities having a fractalesque
manner in their layout. This is only the case if a conscious layout of the city was not planned
out but rather simply grew outward as population grew. To more easily explain this, picture the
2-dimensional top view of a tree’s branches rather than the side view. Many branches
conglomerate in the middle but then spread out and disperse as the distance from the center
increases. Cities follow this self-organizing pattern as they disperse from urban to suburb to
rural. Physical limitations come into play in both cases and explain the asymmetry. Take the
city of Boston for example. It branches to the west but is limited by the Atlantic Ocean to the
east. To correlate with a growing tree, if the tree were growing in close proximity to an infinitely
tall wall, it wouldn’t be able to branch out any farther in that direction. Physical geographic
fractals appear in many cases but the intention of them other than as efficient is unknown.
Bringing the discussion to present-day, the United States government has a branching
layout of power. We’ve been taught this since grade school when we learn about the three
branches of government in our representative democracy. Because the same idea can be
applied to all three branches, the fractal nature of one can confirm the fractal nature of the
whole system. Let’s take the legislative branch into consideration. The head of the branch is
Congress which branches off into the House of Representatives and the Senate. The House of
Representatives represents their individual states’ opinions and state legislation. The State
Representatives each represent one of the districts they are elected to be the head of. Each
district is made up of a few towns who organize their leadership into a town council of a mayor
that represents the individual opinions of the citizens. At this point, we are 7 levels of
branching deep from the head of the legislative power. Each time the system branches off, the
influence of the level is decreased but the number of members in the branch is increased. 1/f
frequency appears once again. A conclusion can be made that the system as a whole operates
in branches that falls under the US government as a whole, the trunk of the tree that is the
United States representation.
Religion and mythology began the blatant interpretation of human society and nature
as a tree. This idea spread and manifested itself into social, geographic, and political aspects of
civilization and continues to subconsciously influence the human race as an underlying driving
force. Many of the experts in the field of self-organization may argue that a trickle down
hierarchy goes against the fundamental rule of self-organization but the evidence shows that
the structure of the hierarchy is fractal as it repeats and divides on many levels as a tree does
when it grows. Like a tree, the more branching a civilization has in the aforementioned aspects,
the larger it has grown to be. It cannot be known for sure why the similarity between the
structure of nature and the “artificial” structure of humanity exists but the resemblances exists
in our everyday lives in many yet we fail to see the big picture because of our seeming
insignificance in the grand scheme of things. Structures develop which display 1/f frequency
as energy comes from one central source and branches out many times, losing energy each
time. By living our everyday lives in the system that is human culture, we unknowingly and
sometimes unwillingly self-organize into a fractalesque civilization.
Excellent writing, great ideas. I thought you missed out on the most important
aspect of fractal trees, which is scaling. If you simply wanted to maximize surface area,
you would just have many small tubes. If you just want to maximize flow rate, you just
have one big pipe. But if you want to maximize both, you need a fractal tree in which the
pipe diameter scales in a nonlinear or log relation. That scaling characteristic means
that many of the things that at first seem tree-like, such as a military hierarchy, are not.
Anyhow that is just a minor aside. Great paper, grade = A.
One big pipe maximizes flow rate
Many small tubes maximize surface area
References
1) Wikipedia/ Tree of Life. (n.d.). Retrieved March 26, 2014 from Wikipedia:
http://en.wikipedia.org/wiki/Tree_of_life
2) Eglash, R. (1999). African Fractals: Modern Computing and Indigenous Design. New
Brunswick, New Jersey: Rutgers University Press.
3) Wikipedia/ Hunter-gatherer. (n.d.). Retrieved March 26, 2014 from Wikipedia:
http://en.wikipedia.org/wiki/Hunter-gatherer
4) Wikipedia/ Feudalism. (n.d.). Retrieved March 26, 2014 from Wikipedia:
http://en.wikipedia.org/wiki/Feudalism
5) Kodiak Island Borough School District. (2005). feudalism diagram illustration. Retrieved
from:
http://moodle.kibsd.org/m/pluginfile.php/23302/mod_page/content/9/feudalism%20
diagram%20illustration.png
6) Wikipedia/ River civilization. (n.d.). Retrieved March 26, 2014 from Wikipedia:
http://en.wikipedia.org/wiki/River_civilization
7) Fractal Foundation. (2013). Fractal Rivers. Retrieved from:
http://fractalfoundation.org/resources/fractivities/fractal-rivers/