The document discusses several concepts related to sacred geometry and fractals in nature. It provides examples of fractal patterns found in plants, ice crystals, lightning, and more. Specific geometric shapes and patterns discussed include the vesica piscis, seed of life, egg of life, flower of life, tree of life, and fruit of life. The document explains that fractals and sacred geometry can be seen throughout nature and the structures that evolve according to these patterns are highly efficient.

1. Design in Nature
Presented by Debsree Mandal
Assistant Professor,
Department of Architecture, Chittagong University of Engineering and Technology, Chittagong, Bangladesh
Course: Design Theory

2. Design in Nature is an elegant exposition of a unifying
principle , so simple that it demystifies our
comprehension of the ‘law’ of the universe.
Everything—from biological life to inanimate
systems—generates shape and structure
and evolves in a sequence of ever-improving designs in
order to facilitate flow, the more complex architecture
of animals evolve to cover greater distance per unit of
useful energy, or increase their flow across the land----
River basins, cardiovascular systems, and bolts of
lightning are very efficient flow systems to move a
current—of water, blood, or electricity.
Book: Design in Nature
By ADRIAN BEJAN and J. PEDER ZANE

3. Fractals
Fibonacci Sequence
Golden Ratio
Sacred Geometry

4. Fractals Found in Nature, By Shea Gunther
Fractals, first named by mathematician Benoit Mandelbrot in 1975, are special mathematical
sets of numbers that display similarity through the full range of scale — i.e.,
they look the same no matter how big or how small they are.
Another characteristic of fractals is that they exhibit great complexity driven by simplicity — some of
the most complicated and beautiful fractals can be created with an equation populated with just a
handful of terms.
One of the amazing characteristics is ubiquity in nature.
The laws that govern the creation of fractals seem to be found throughout the natural world.
Pineapples grow according to fractal laws and ice crystals form in fractal shapes, the same ones that
show up in river deltas and the veins of your body. It's often been said that Mother Nature is a hell of
a good designer, and fractals can be thought of as the design principles she follows when putting
things together.
Fractals are hyper-efficient and allow plants to maximize their exposure to sunlight and
cardiovascular systems to most efficiently transport oxygen to all parts of the body.
Fractals are beautiful wherever they pop up, so there's plenty of examples to share.

5. Photo: Rum Bucolic Ape/flickr
Try not to fall into this closeup photo of Romanesco
broccoli.
Each of the smaller buds is made up of even smaller
buds. Here's another.

6. Photo: Aidan M. Grey/flickr
You can see some of the same fractality in the spirals of
pinecone seeds. Fractals is in how this plant's leaves grow around each other.
Photo: Genista/flickr

7. Photo: Bert Hickman/Wikimedia Commons
This block of plexiglass was exposed
to a strong current of electricity that
burned a fractal branching pattern
within. This can be best thought of as
bottled-lightning.

8. Photo: Schnobby/Wikimedia Commons
That same pattern
shows up all over the
place. Here are ice
crystals forming.

9. Photo: Abe Bingham/flickr
Photo: Fabio Mascarenhas/flickr

10. Photo: i5a/flickr
We see fractals in water drops.
Photo: NatJLN/flickr

11. Photo: Air bubbles. Woodley Wonderworks/flickr
So, They're everywhere.
A great example of how fractals can be
constructed with just a few terms is the
Mandelbrot Set.
Named for its discoverer, mathematician Benoit
Mandelbrot, the Mandelbrot Set describes a
fantastical shape that displays amazing self-
similarity no matter what scale it is looked at
and can be rendered with this simple equation:
zn+1 = zn
2 + c
Basically it means that you take a complex
number, square it, and then add itself to the
product, over and over again. Do it enough
times, translate those numbers to colors and
locations on a plane, and, you've got yourself a
beautiful fractal!
Video Links:
1. https://www.youtube.com/watch?v=w_MNQBWQ5DI
2. https://youtu.be/0jGaio87u3A
3. https://youtu.be/ovJcsL7vyrk
4. https://www.youtube.com/watch?v=WFtTdf3I6Ug
5. https://www.youtube.com/watch?v=VjzkW1IlVI4

12. https://www.youtube.com/watch?v=w_MNQBWQ5DI

13. Sacred Geometry Art,
Symbols & Meanings
by Randall Morgan
• Sacred Geometry is often referred to as the
“architecture of the universe”, it is found throughout the
natural world.
• It is all around us and is one of the very few subjects
that satisfy both the left brain and right brain
hemispheres simultaneously. It satisfies the left brains
desire for logical, sequential and objective data. It also
satisfies the right brains desire for random, intuitive and
subjective data.
• The Graphic shows all of the basic Sacred Geometry
shapes.

14. 1. Vesica Piscis
• Vesica Piscis is a mathematical shape formed by intersecting two
identical circles so that the center of each circle intersects the
perimeter of the other.
• The vesica piscis is commonly used for Venn Diagrams and in
various art and in seals organizations.
• Various other symbols can be derived from the vesica piscis
including the Ichthys, also known as the “Jesus Fish”, the triquetra
symbol, and the Reuleaux triangle. It has also been a symbol used by
Freemasons for many years.
• Historically, the vesica piscis has been used as a system of
proportions for architecture, illustrated in the works of Vitruvius.

15. 3. Egg of Life
The Seed of Life is a universal symbol that also represents the seven days of
creation.
It is found in all of the major religions and can be seen in many sites around the
world, such as churches, mosques, prayer books and ancient temples.
The two dimensional projection of the seed of life contains seven overlapping
circles. It has been used for centuries as a symbol of blessing and protection.
2. Seed of Life
A symbol that has been used to represent new life, rebirth and fertility.
The Egg of Life is the second iteration of a process that constructs the Flower of
Life. Adding six additional circles to the seed of life you are able to produce the
Egg of Life.
This can also be formed by the eight spheres contained within the three
dimensional Metatron’s Cube.

16. 4. Flower of Life
• The Flower of Life was known around the world in ancient times and
has been found in Ireland, Turkey, Egypt, Greece, China, Israel, Germany,
England, Tibet, Japan and Sweden.
• The typical depiction Flower of Life always stops after 19 circles, the
remaining circles are hidden outside the bounds of the outer circle. In the
past this image and knowledge related to the Flower of Life was so sacred
that they couldn’t allow it to become common knowledge. Out of the
complete Flower of Life pattern a new shape emerges; the “The Fruit of
Life”.
• The Flower of Life is said to be the actual blueprint of the universe
continuing the basic design of every atomic and molecular structure, life
form, etc; essentially everything in existence.
• Modern science and quantum physics are confirming the cosmic
significance of these ancient sacred geometric forms which represent the
building blocks of our physical universe.
• The ancients knew about the energetic nature of our existence. Other
sacred patterns such as the Egg of Life, Seed of Life and the Tree of Life also
exists within the Flower of Life pattern.

17. 5. Germ of Life
The germ of life is the first full construction that is taught by Justin The Cirler.
This is a magical little construction that naturally falls out with seven simple steps.
This can be done with just rusty compass (compass that does not change size) in seconds.
Ancient peoples would have come discovered this very quickly and would adored if for its
organizational properties and simplicity.
The one, the Sun, the only, is first to
appear
It then becomes two and a closed eye can
see no fear.
The eye opens
and sees allMoon's light covers her night,
then daylight shows his might.
This flower now blooms in the Fall.

18. 6. Tree of Life
The Tree of Life is another popular universal symbol.
It represents numerous systems across varying cultures and religions. Like all the other symbols in
this list, it is not identified by a single culture and it has been used around the world for centuries.
So what does the Tree of Life represent? A connection to everything including the things we
cannot see or the void beyond. It reminds you that you are not alone in the Universe but rather
part of a vast interconnected network.
The Tree of life is considered to be a map of the universe and the psyche, the order of the creation
of the cosmos, and a path to spiritual illumination.
The Tree of Life provides a hierarchical structure for all of the forces in the Universe. It can also be
used as a road map of one’s soul. The 10 spheres are called the “Sephiroth” translating to
emanation. These are connected by different paths. The ten spheres represent the ten archetypal
numbers of the Pythagorean system. There are said to be 32 paths on the Tree of Life.
The first Sephira on the Tree of Life is at the top. It represents cosmic consciousness. The Sephira
at the base represents the material world. The rest of these Sephiroth represent different qualities
of the Soul. These can be divided into three pillars; the Pillar of Severity, The pillar of Mildness and
the Pillar of Mercy.

20. 7. Fruit of Life
The 13 spheres represent an extremely powerful sacred geometric pattern known as
the Fruit of Life, considered the Holy of Holies of Sacred Geometry because it's hidden
within the ancient and well-known Flower of Life pattern.
The fruit of life is composed of 13 spheres; this is actually the 2d representation of a 3d
structure. Thirteen represents unity and transition between worlds / dimensions.
Those of you who play an instrument know the chromatic scale of 12 notes the thirteenth
note is actually repeating the first note but on a higher frequency; when you attain a higher
octave you enter a higher dimension.
If we connect all the Centers of the 13 circles the result is 78 lines which create a structure
known as Metatron's Cube. This structure contains all five platonic solids, these three-
dimensional figures and their different combinations reveal every possible geometric law
forming the physical reality we are experiencing.
The spheres of the Fruit of Life represents the female movements or elements of creation
and provide the field for the 78 ray like male movements of creation. The geometry of
Metatron's Cube is set to underlie what modern physics calls the quantum vacuum or void
and is fundamental to the creation process at the quantum level. What we're talking about
here is what's been called zero-point, life force or bio force energy.

21. 8. Metatron’s Cube
One of the most fascinating aspects of sacred geometry is the symbol known as Metatron’s Cube. So
who is Metatron?
If you investigate, Metatron was an archangel who was mentioned in Islamic, Judaic and Christian
medieval mythologies. He was considered to be the scribe of God, this would make him the equivalent
of the ancient Egyptian scribes of the gods known as Thoth. According to legend a scribe of God would
understand the basic principles of creation which are almost always associated with sacred geometry.
Many times the Archangel Metatron is pictured with or holding a cube.
The graphic known as Metatron’s Cube didn’t show up until later when a Medieval Italian
Mathematician Leonardo Pisano, discovered Metatron’s Cube. He read the history and legends of
Metatron and was also familiar with sacred geometry and was probably an initiate in one of the schools
that held those secrets.
Metatron’s Cube traces back to nature's first pattern, and the 13 circles that are found inside the fourth
circle in Nature’s first pattern. When you connect the centers of all the 13 circles, you get the shape
known as Metatron’s Cube. Leonardo Pisano also discovered that you could create all 5 of the platonic
solids within Metatron’s Cube. Metatron’s Cube is a transcendental form and beautifully illustrates the
mental universe through the unfolding of 2-dimensional realities into 3 dimensional realities.
The Hermetic axiom reads “all is mind, the universe is mental” and Metatron’s Cube is teaching us about
this conceptual mental nature of the universe and the current experiments in quantum physics are also
teaching us this exact same thing. Without first being a conceptual equivalent in consciousness nothing
could exist. Sacred geometry is the creator’s conceptual architecture on which all things precipitate.

23. 9. Grid of Life
The star tetrahedron is the basis of the 64 grid.
tetrahedron also known as the Grid of Life.
This is the masculine equivalent to the Flower of Life
pattern.
As the name suggests, this shape is made up of 64
tetrahedrons, which as you know is one of the platonic
solids.

24. When the 64-tetrahedron is overlaid on the flower of life this represents a powerful concept; the spheres represent
space and the lines represent where space and time come together.
One of the most fascinating aspects of the 64 tetrahedron is the number 64 itself and how it appears throughout
the natural world.
Here are a few examples:
-There are 64 codons in human DNA.
-64 is the number of cells we have before the cells start to bifurcate (differentiate) after conception.
-64 is the fundamental number in computer memory and bits of code
-64 is encoded in the Tetragrammaton within the Hebrew Bible, which is the four letter theonym YHWH that means
God in Hebrew.
-64 is the number of generations from Adam until Jesus.
-64 manifestations of Lord Shiva in Hinduism
-64 squares in chess and checker boards
-64 hexagrams in the I Ching
-64 tantras which is a form of Hinduism
-64 is the maximum number of strokes in any Chinese character.
This metaphysical symbol can produce many trees of life which radiate inward, this is why the 64 tetrahedron is
symbolic of linking up ones individual paths in harmony with our soul family. It is said that connecting with your
soul / star family will amplify each individual's energy to accomplish and manifest one's goals. A true symbol of the
mastermind principle of harmony with among a group of individuals.

25. 10. Vector Equilibrium 1 11. Vector Equilibrium 2
The Vector Equilibrium center is primal
"emptiness." It is a mathematical anomaly where
the normal laws of the space/time continuum
break down. It is not a symbol of ultimate order.
It looks like a very rational, orderly system, but it
is ultimately irrational. According to Fuller, it is a
zone of neutral resonance where waves can pass
through waves without interference. Yet, it never
physically exists as a structure because nature
abhors a vacuum.
Vector Equilibrium emanates/condenses from a center in twelve fundamental directions. This emergent energy
moves outward through space/time in the form of a cuboctahedron, alternating with its mathematical
reciprocal, an octahedron-within-a-cube. It is a truncated cube with 50 symmetrically positioned topological
features. Vector Equilibrium has the same surface area as a sphere, yet contains no volume, i.e. it contains
"nothing."
The Vector Equilibrium system has 12 vertices, 8 triangular faces, 24 edges, and 32 planes. It is an
omnidirectional equilibrium symbolically and physically speaking. Thus, it is a perfect symbol for "holding the
tension of the opposites," or "uniting the opposites." Yet, it is more than a metaphor. It is an archetypal image
which connects the matrix with the universe or the universe with the matrix.

26. https://www.youtube.com/watch?v=b7AlKobC4bo
Vector Equilibrium with
admiration on greatest work
of Nassim Haramein and
Buckminster Fuller.

27. The shape known as a 'Torus' is a type of vortex. So what is a torus?
The word “torus” comes from the Latin word meaning swelling. In sacred
geometry it is the first shape to emerge from the Genesis Pattern
(how God created earth in 6 days).
The torus is found in everything from atoms, to life forms and even in all
cosmic bodies such as stars and galaxies. It is a primary shape in existence.
For many years ‘seers’ have taught that the human aura appears as a series
of nested torus formations around the body. Energy flows through the center
of the body and loops around to connect the feet and head.
The flow from the feet to the head is bi-directional.
The energy is flowing through the surface of the torus and inside in a spiraling pattern, this is why the sacred geometry
shape is shown with curves lines throughout the middle, while also adding the illusion of a 3d perspective to the 2d
depiction.
The Torus is a 2d depiction of a 3 dimensional shape, like many other sacred geometry forms. The 3d shape is known as a
horn torus. This can be mathematically described here.
12. Torus

28. The Merkaba symbol (also spelled Merkabah) translates to light, spirit, body.
The symbol consists of 2 intersecting tetrahedrons that rotate in opposite directions, this creates an energy
field that is commonly referred to as a light body.
Merkavah mysticism is an early school of Judaism, practiced between 100 BCE - 1000 CE. The teachings were
based on visions found in the Book of Ezekiel and hekhalot literature. These stories speak of ascents into the
heavens and to the Throne of God.
Everyone has access to their own personal Merkaba or vehicle of light with practice in meditation. It is said
that once one has access to their Merkaba it can provide a powerful protection and transport your
consciousness to higher dimensions. The Merkavah symbol can remind us of the potential power we hold
when we unite our bodies energy to Source.
This symbol combines opposing energies in perfect harmony and has allegedly been used by ascended
masters to connect to higher realms.
In modern esoteric teachings, the Merkaba is considered an interdimensional vehicle. It is also known as a
star tetrahedron and can be imagined as a 3-dimensional Star of David.
13. Merkaba

29. Merkaba

31. https://youtu.be/XZmKDkj7P58

32. Fibonacci Sequence In Nature
Fibonacci (real name Leonardo Bonacci) was a mathematician who developed the Fibonacci Sequence. The sequence
is found by adding the previous two numbers of the sequence together. It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34...
And on it goes. This pattern can also be seen as:
The Fibonacci Sequence is found all throughout nature, too. It is a natural occurrence that different things develop
based upon the sequence.

33. 1. Shells
As you may have guessed by the curve in the box example above, shells follow the progressive proportional
increase of the Fibonacci Sequence. Shells are probably the most famous example of the sequence because the
lines are very clean and clear to see. They are also fun to collect and display.
2. Trees
Tree -- we see them everywhere, but do you look and
analyze the structure of how the branches grow out
of the tree and each other?
If you did, you would see the Fibonacci Sequence
evolve out of the trunk and spiral and grow the taller
and larger the tree becomes. Some truly majestic
trees are in existence today, utilizing this pattern.

34. 3. Flower Pistils
The part of the flower in the middle of the petals (the pistil) follows the Fibonacci Sequence much more intensely than
other pieces of nature, but the result is an incredible piece of art.
The pattern formed by the curve the sequence creates used repeatedly produces a lovely and intricate design.

35. • 4. Flower Petals
• Flowers of all kinds follow the pattern, but roses are used here as an example of the Fibonacci Sequence.
• I like it because the petals aren't spread out and the spiral is more obvious and clear, like with the shell.
• The petals unfold more and more and the sequence increases. Roses are beautiful (and so is math).

36. • 5. Leaves
Leaves follow Fibonacci both when growing off
branches and stems and in their veins.
I, personally, find the veins much more
interesting and amazing to look at. Similar to a
tree, leaf veins branch off more and more in the
outward proportional increments of the
Fibonacci Sequence.

37. • 6. Storms
Specifically hurricanes and tornadoes, many
storm systems follow the Fibonacci Sequence.
I suppose this is not beautiful, but more
interesting. On a map, at least, hurricanes look
cool. I guess we could say this example proves
math can be beautiful and destructive.

38. 7. You!
Yes! You are an example of the beauty of the Fibonacci
Sequence.
The human body has various representations of the Fibonacci
Sequence proportions, from your face to your ear to your
hands and beyond!
You have now been proven to be mathematically gorgeous, so
go forth and be beautiful! ...and maybe think math is a little bit
better than you first thought?

39. Golden Ratio Manifests in Nature
The universe may be chaotic and unpredictable, but it's also a highly organized physical realm bound by
the laws of mathematics. One of the most fundamental (and strikingly beautiful) ways these laws
manifest is through the golden ratio.
The golden ratio (often represented by the Greek letter φ) is directly tied to a numerical pattern known as
the Fibonacci sequence, which is a list composed of numbers that are the sum of the previous two
numbers in the sequence. Often referred to as the natural numbering system of the cosmos, the
Fibonacci sequence starts out simply (0+1= 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8...), but before long, you'll find
yourself adding up numbers in the thousands and millions (10946+17711=28657, 17711+28657=46368,
28657+46368=75025...) and it just keeps going on forever like that.
When a Fibonacci number is divided by the Fibonacci number that came before it, it approaches the
golden ratio, which is an irrational number that starts out as 1.6180339887... and, once again, goes on
forever.
When the golden ratio is applied as a growth factor (as seen below), you get a type of logarithmic spiral
known as a golden spiral.

40. A chameleon tail is famous for its tight
spiraling shape. (Photo: Ryan M.
Bolton/Shutterstock)
A seashell is one of the most well-known
examples of the golden ratio spiral in
nature. (Photo: Tramont_ana/Shutterstock)
The curled up fronds of a young fern are
known as fiddleheads. (Photo:
Zamada/Shutterstock)
A whirlpool exhibiting a golden ratio
spiral. (Photo: Elaine Davis/Shutterstock)
A spiral aloe plant sits in a gardening
pot. (Photo: PhotoSky/Shutterstock)
The golden ratio of growth seen
in a sunflower head. (Photo:
Portogas D Ace/Shutterstock)

41. When a flower hasn't yet bloomed, it's easy to see
evidence of the golden ratio. (Photo: Romantsova
Olga/Shutterstock)
You can see the spiral of this Comfrey
flower's stalk. (Photo: Mikhail
Melnikov/Shutterstock)
The spiraling bloom of a calla lily.
(Photo: Lynn Watson/Shutterstock)
A spiky shell with a golden ratio spiral. (Photo:
Fontana/Shutterstock)
This spider web uses a spiral
shape. (Photo: mycteria/Shutterstock)
There are many golden ratios among these
curly flower petals. (Photo: Ian
Grainger/Shutterstock)

42. The fractal spirals of Romanesco
broccoli (Brassica oleracea). (Photo:
Sergey Skleznev/Shutterstock)
Snail shells are a lovely example of the
golden ratio in nature. (Photo:
vvoronov/Shutterstock)
Despite their tumultuous nature, ocean
waves are another example of the
golden ratio manifesting in
nature. (Photo: irabel8/Shutterstock)
Golden ratio spirals as
seen from the bottom of
a pinecone. (Photo:
bzanchi/Shutterstock)
The spiral of Hurricane Isabel in
2003. (Photo: Mike Trenchard/NASA)

43. https://www.youtube.com/watch?v=Ezd4AcC3uZ4
Design Inspired by Nature

44. 1. https://lucyadams99.wordpress.com/2011/09/06/fractals-all-around-us/
2. http://designcrushblog.com/2019/01/09/print-edition-january-2019/
3. http://castleofcostamesa.com/waldorf-days/wednesday-morning-craft-group/making-t-shirt-yarn-
projects-week-2-monday-morning-september-15-2014/
4. https://www.treehugger.com/amazing-fractals-found-in-nature-4868776
5. https://blazepress.com/2014/07/46-incredible-things-may-never-seen/
6. https://www.tokenrock.com/explain-tree-of-life-160.html
7. https://i.pinimg.com/originals/15/7c/e5/157ce5c490d548b0e170e849d6979e5c.png
8. https://blog.etemetaphysical.com/seedoflife/
9. http://www.turningcircles123.com/seed-of-life/
10. http://www.turningcircles123.com/seed-of-life/
11. https://www.cosmic-core.org/free/article-65-number-the-hexad-part-5-six-around-one-flower-of-
life/
12. https://pardesco.com/blogs/news/sacred-geometry-art-symbols-meanings
13. http://thevectorequilibrium.blogspot.com/2012/01/vector-equilibrium.html
14. https://taquionica.wordpress.com/2016/03/03/solidos-platonicos-representacion-de-los-
elementos/comment-page-1/#comments
15. https://www.soul-flower.com/blog/metatrons-cube-meaning-sacred-geometry/
16. https://www.soul-flower.com/blog/platonic-solids-meaning-sacred-geometry/
17. https://www.theodysseyonline.com/7-beautiful-examples-fibonacci-sequence-nature
18. https://www.housemixblog.com/2017/12/19/is-there-proof-god-exists/
19. https://www.treehugger.com/how-golden-ratio-manifests-nature-4869736
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