Sierpinski Triangle This is the fractal we can get by taking the midpoints of each side of an equilateral triangle and connecting them. The iterations should be repeated an infinite number of times Suppose the coast of Britain is measured using a 200 km ruler, specifying that both ends of the ruler must touch the coast. Now cut the ruler in half and repeat the measurement, then repeat again: COASTLINE PARADOX

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COURSE CODE:ARCP689
WEEK NO.: 8
LECTURE DETAIL :
Fractal Geometry Theories
COURSE INSTRUCTOR: Mostafizur Rahman UID: 19838, LPU, PUNJAB, INDIA
CAP CATEGORY:
EXAM CATEGORY:
LSAD : AD01 : ARCHITECTURE

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LSAD : AD01 : ARCHITECTURE Slide 02: Structure of Presentation
Sierpinski
Triangle
This is the fractal we
can get by taking the
midpoints of each
side of an
equilateral triangle
and connecting
them. The iterations
should be repeated
an infinite number
of times.

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Lewis Fry Richardson
(1881-1953) :
COASTLINE PARADOX
https://www.youtube.co
m/watch?v=I_rw-
AJqpCM
Suppose the coast of Britain is measured using a 200 km ruler,
specifying that both ends of the ruler must touch the coast.
Now cut the ruler in half and repeat the measurement, then
repeat again:

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A fractal often has the following features:
• It has a fine structure at arbitrarily small scales.
• It is self-similar (at least approximately).
• It is too irregular to be easily described in
traditional Euclidean geometric language.

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What is the Butterfly Effect?
In chaos theory, the butterfly effect is the sensitive
dependence on initial conditions in which a small
change in one state of a deterministic nonlinear
system can result in large differences in a later state.
Can a butterfly really cause a hurricane?
The Butterfly Effect: This effect grants the power to
cause a hurricane in China to a butterfly flapping its
wings in New Mexico. It may take a very long time,
but the connection is real. If the butterfly had not
flapped its wings at just the right point in space/time,
the hurricane would not have happened.

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What is the Chaos Theory?
Chaos theory is a field of study in mathematics which
studies the behavior of dynamical systems that are
highly sensitive to initial conditions—a response
popularly referred to as the butterfly effect.
MULTIVERSE

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MULTIVERSE
The multiverse is a theory in which our universe is not
the only one, but states that many universes exist
parallel to each other. These distinct universes within
the multiverse theory are called parallel universes
Level 1: If you go far enough, you’ll get back home
Level 2: If you go far enough, you’ll fall into
wonderland
Level 3: If you stay where you are, you’ll run into
yourself

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CITIES AND FRACTAL GEOMETRY

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organic towns when viewed in
plan form resemble cell
growth, weaving in and out of
the landscape, closely
following the terrain and
other natural features,
embodying the technology of
movement through main
transport routes, like spider
webs or tree-like forms
focused on centers which
usually contain the origin of
growth

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In contrast, planned
towns display a
geometry of straight
lines and smooth
curves, built on a
directness of
movement which can
only be imposed from
above, embodying
some sense of man's
direct control over
nature through
technology.

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Wherever planned
development has
taken place, man has
invoked the doctrine
of visual order and
imposed simple,
regular geometrical
forms or shapes on
cities

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A circular and fortified
town, divided by two
axes into four quarters
where the pictures in
each
symbolize the usage of
these areas. The plan
was embodied as a
relief on
the wall of a temple in
Nimrud (in present-
day Iraq) 2000BC

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A pure geometry

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The camps used by
workers to
construct the
pyramids and other
monuments in ancient
Egypt were laid
out according to the
strict principles of the
grid

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FRACTAL GEOMETRY
CITIY IN THE SKY
FRACTAL TEMPLE, IRANIAN