hi guys my seven-year-old little cousin
sent me this drawing the other day
that’s very cute right but men look at
how smooth her landscape is I mean this
the the mountains look like triangles
the sky is a straight line but I don’t
blame her I mean she’s completely biased
by Euclidean geometry right you studying
at school and I have nothing again
against it but to my mind it tends to
oversimplify our perception of nature I
mean have you guys ever seen a perfect
square or perfect triangle a perfect
circle in nature think about it I mean
we just have to face it in nature
nothing is flawless except Beyonce but
we all know that now the truth is we
live in a complex irregular world where
the movements of streams and rivers and
the branching of neurons and blood
vessels cannot be reduced to idealized
shapes so let’s all take a step back
from Euclidean geometry to step up to
reality enter the the real rough world
that could be measured thanks to fractal
geometry now you see I’m not an expert
I’m not a scientist I’m just a fan of
this guy the late the great Bernama
Mandelbrot who spent his entire life
studying roughness and trying to develop
a new field of geometry fractal geometry
I’m sure some of you are wondering what
fractals are right well fractals can be
found in the most dangerous dark places
places that usually people don’t want to
go to and by that i mean the office the
other day and it’s a true story a couple
of days ago I was at the office and I
came across this plant
it’s called a fern and my first thought
was wow man what a messy plant look at
it but as I looked closer I realized it
was a fractal now if we take a look at
one of its leaves and we zoom into it
will realize that the little leaves are
the same have the same shapes as the
bigger ones and this is the first
characteristic of fractals it’s called
self similarity as one pattern repeats
itself at different scales now second
property is a bit more complicated it’s
called non integer dimensions or fractal
dimensions now we can all agree on this
we live in a three-dimensional world
right from the zero dimensional point to
the one-dimensional line to the
two-dimensional plane figures like
triangles the three-dimensional solids
like pyramids let’s say but fractals
work differently they’re actually in
between dimensions now if we take for
example the digital representation IV at
a fractal landscape a mountain for
example it’s actually going to be
between dimension 2 and 3 and the more
heaps and hills and roughness it
contains the more it approaches
dimension 3 I take a look at this
mountain it’s actually a
computer-generated mountain and it looks
so real right it looks so real because
we know the dimension of this mountain
is to point 15 and we have applied to an
algorithm to generate this image now
what happens if we crease this dimension
to let’s say 2.8 it doesn’t look real
anymore so actually thanks to fractal we
can create graphical images of nature
using nothing out of nothing except
their fractal dimensions and this has
actually changed the way we make films
and use special effects some of the
graphics you have seen you may have seen
in Star Wars of Star Trek were made
using fractal geometry well as you can
see
fractals are extraordinary because they
have many many applications in
engineering science arts astrophysics
even but there’s one that really got me
very very excited three years ago a team
of scientists from the Max Planck
Institute for intelligent systems have
found out a way to identify cancer cells
using fractal geometry according to them
the roughness of cells is an indicator
of their aggressiveness you see the one
on your right it’s a pancreas cancer
cell is more rough and more irregular on
the edges and it happens to be more
aggressive so it’s it’s only a start and
hopefully this research is going to
continue but we know today that this
kind of method is cheaper faster and far
more accurate that the established ones
now you see to sum it up fractals made
us have a better understanding of how
nature works of how our body works but
it doesn’t tell you why I love them the
reason I fell in love with fractals is
this function yep FC of Z equals Z
square plus I see some of you got scared
over here but don’t worry I’m not going
to go into mathematical details just
just bear in mind that this is a very
very simple function although it may not
look like it it’s a simple function
simple function and yet its graphical
representation is one of the most
incredible sophisticated and complex
thing I’ve ever seen on a complex plane
it’s a fractal and it’s called the
Mandelbrot set and so I suggest we zoom
into it and see what happens actually I
have a fractal animation that was
created by very talented developer
called Michael hug and who kindly
allowed me to share it
with you today so we’ll see it and the
yep so this my friend is what infinity
looks like literally infinity if you
have a computer that is powerful enough
you can go on forever and ever and ever
and you will always find this shape the
black shape and the beauty of it is that
at each different scale you will find
shapes that had never appeared before
that’s the beauty of it so actually
fractals have changed the way look at
things the way I look at life I try to
accept embrace and even celebrate the
irregularities complexity and roughness
of my life because at the end of the day
you never know what good may come out of
it they can be a source of beauty even
infinite beauty so if only for this
reason please next time you see kids
drawing make sure you tell them that
mountains are not triangles thanks [Applause]
sent me this drawing the other day
that’s very cute right but men look at
how smooth her landscape is I mean this
the the mountains look like triangles
the sky is a straight line but I don’t
blame her I mean she’s completely biased
by Euclidean geometry right you studying
at school and I have nothing again
against it but to my mind it tends to
oversimplify our perception of nature I
mean have you guys ever seen a perfect
square or perfect triangle a perfect
circle in nature think about it I mean
we just have to face it in nature
nothing is flawless except Beyonce but
we all know that now the truth is we
live in a complex irregular world where
the movements of streams and rivers and
the branching of neurons and blood
vessels cannot be reduced to idealized
shapes so let’s all take a step back
from Euclidean geometry to step up to
reality enter the the real rough world
that could be measured thanks to fractal
geometry now you see I’m not an expert
I’m not a scientist I’m just a fan of
this guy the late the great Bernama
Mandelbrot who spent his entire life
studying roughness and trying to develop
a new field of geometry fractal geometry
I’m sure some of you are wondering what
fractals are right well fractals can be
found in the most dangerous dark places
places that usually people don’t want to
go to and by that i mean the office the
other day and it’s a true story a couple
of days ago I was at the office and I
came across this plant
it’s called a fern and my first thought
was wow man what a messy plant look at
it but as I looked closer I realized it
was a fractal now if we take a look at
one of its leaves and we zoom into it
will realize that the little leaves are
the same have the same shapes as the
bigger ones and this is the first
characteristic of fractals it’s called
self similarity as one pattern repeats
itself at different scales now second
property is a bit more complicated it’s
called non integer dimensions or fractal
dimensions now we can all agree on this
we live in a three-dimensional world
right from the zero dimensional point to
the one-dimensional line to the
two-dimensional plane figures like
triangles the three-dimensional solids
like pyramids let’s say but fractals
work differently they’re actually in
between dimensions now if we take for
example the digital representation IV at
a fractal landscape a mountain for
example it’s actually going to be
between dimension 2 and 3 and the more
heaps and hills and roughness it
contains the more it approaches
dimension 3 I take a look at this
mountain it’s actually a
computer-generated mountain and it looks
so real right it looks so real because
we know the dimension of this mountain
is to point 15 and we have applied to an
algorithm to generate this image now
what happens if we crease this dimension
to let’s say 2.8 it doesn’t look real
anymore so actually thanks to fractal we
can create graphical images of nature
using nothing out of nothing except
their fractal dimensions and this has
actually changed the way we make films
and use special effects some of the
graphics you have seen you may have seen
in Star Wars of Star Trek were made
using fractal geometry well as you can
see
fractals are extraordinary because they
have many many applications in
engineering science arts astrophysics
even but there’s one that really got me
very very excited three years ago a team
of scientists from the Max Planck
Institute for intelligent systems have
found out a way to identify cancer cells
using fractal geometry according to them
the roughness of cells is an indicator
of their aggressiveness you see the one
on your right it’s a pancreas cancer
cell is more rough and more irregular on
the edges and it happens to be more
aggressive so it’s it’s only a start and
hopefully this research is going to
continue but we know today that this
kind of method is cheaper faster and far
more accurate that the established ones
now you see to sum it up fractals made
us have a better understanding of how
nature works of how our body works but
it doesn’t tell you why I love them the
reason I fell in love with fractals is
this function yep FC of Z equals Z
square plus I see some of you got scared
over here but don’t worry I’m not going
to go into mathematical details just
just bear in mind that this is a very
very simple function although it may not
look like it it’s a simple function
simple function and yet its graphical
representation is one of the most
incredible sophisticated and complex
thing I’ve ever seen on a complex plane
it’s a fractal and it’s called the
Mandelbrot set and so I suggest we zoom
into it and see what happens actually I
have a fractal animation that was
created by very talented developer
called Michael hug and who kindly
allowed me to share it
with you today so we’ll see it and the
yep so this my friend is what infinity
looks like literally infinity if you
have a computer that is powerful enough
you can go on forever and ever and ever
and you will always find this shape the
black shape and the beauty of it is that
at each different scale you will find
shapes that had never appeared before
that’s the beauty of it so actually
fractals have changed the way look at
things the way I look at life I try to
accept embrace and even celebrate the
irregularities complexity and roughness
of my life because at the end of the day
you never know what good may come out of
it they can be a source of beauty even
infinite beauty so if only for this
reason please next time you see kids
drawing make sure you tell them that
mountains are not triangles thanks [Applause]
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