Author: Eddie Woo

Fractals
(Eric Sun)

Fractals are everywhere in nature. They are never ending.
They go on forever until the human eye can’t see it anymore. Fractals can be seen
almost everywhere in our environment such as shorelines where they keep splitting
up into various individual rivers and the dividing branches on trees. Fractals
can be enlarged and part of it still resembles the original shape.

Favourite Fractal                                                                                                                                        My favourite fractal is the salt flats
in San Francisco and Bolivia. They may seem normal but a closer look will
reveal that they are full of fractals. It looks normal at first but look closer
and they look amazing but it’s subtle.

#exploremaths 

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#exploremaths
In this lesson I learnt many things such as Donald duck is cool and how maths is cool

I the first video that we watched was all about Pythagoras and his discoveries. The main ideas that I took away from this were: the ratio of an octave being 2:1, how pentagons are really, really, really, cool and finally the overwhelmingly awe-inspiring, inconceivable fact that Mr. Woo just so happened to mention under his breath: Pythagoras suggested that the universe is made of numbers. Now, that may have seemed relatively anti-climactic after all of those big words but when you think about it; the universe being made of numbers is pretty darn amazing. This is especially true as if numbers, on their own, are just things that we conceive, as they are no linger adjectives for nouns, then the entirety of the universe is something that we conceive. So in that sense numbers and the universe are just like infinity; there is no infinity but it is still real even though we can not see it or ever have an infinite amount of anything.

The other things that I mentioned earlier were the pentagram and the octave. These are not as amazing as the conceived universe but they are still pretty exceptional. The pentagram consists completely of fractals, the golden ratio, spiral, rectangle and angle. Either that or it consists completely of illuminati, the devil and that angry goat thing.

Anyway all the things it is made of basically constitute to maths and here is a neat example of a supposedly infinite amount of pentagrams inside a pentagram.

 

Personally I think that there must be a pattersn or rule that tells you how much golden ration tht there is in a shape and that the pentagram is just the most prominent example of the golden ratio in a shape.

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#exploremaths

Fractals are scattered every in nature, from the lightning
that strikes the Earth to our very own lungs. As a line can never really be
straight, they show how the world can be perfect through it’s imperfections.
Many things throughout the world have this property and it can also be known as
iteration or scale symmetry. Personally, I find the fractals found in rivers to
be mesmerising as you can look at them from satellite imagery or through a
microscope to find the same basic shape. 

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#exploremaths

 

In the lesson, we went over some older memories from primary
school and talked about the different types of symmetry. Although we drew some
examples of rotational and reflectional symmetries, the main points of discussion
were scale and translation symmetry. Scale symmetry, as we went on to learn
about this in future lessons, was essentially describing the self-similarity of
shapes. We attempted to show this type of symmetry in our books too, by drawing
a square with many rotating squares inside of it. The remaining type,
translational symmetry or tessellation, was how one shape could be used to fill
an area without leaving any spaces. One example would be, as we discussed in
class, the hexagons of a beehive. Another naturally occurring tessellation is the pineapple as it is, like the beehive, filled with many hexagons. Though
these are irregular shapes, it is still quite interesting to see how nature’s
beauty is based on mathematics. 

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Fractals are never ending, goes on forever, until the human eyes can’t see it anymore. it is one of the most beautiful type of shape that I have ever seen. Fractals can be enlarged and enlarged, part of it still resembling the original shape. Although it sounds unreal and magical, it exists all around us, like the coastline, fern leaves, rivers and tree branches. All of these are wonderful and awesome, but my favorite has got to be the Koch Fractals.

Favorite Fractal

The Koch Fractal is so simple to draw but extremely complex to our eyes. Its hexagons continue on spreading. it is extremely intriguing to our eyes, as all the fractals are. However, what makes this different to others, to me, is the fact that it resembles snowflakes. it shows the beauty of snowflakes, crafted in precise conditions in order to make such beautiful and intricate shape.

#exploremaths

These are the architectures and beings of nature that have become my favorite Golden Ratios.

Golden Ratio in Architecture:

 

1) Parthenon

The Parthenon in Greece follow the golden ratio in different parts of its structure. The entire front face of the Parthenon closely resembles the golden rectangle. Also, the structural beam on top of the supporting poles are proportional to each other, in golden ratio.

2) Notre Dame

Notre Dame in Paris, which was built in between 1163 and 1250 appears to have golden ratio proportions in a number of its key proportions of design. Although it is inaccurate to measure by a photographic source, it is possible to notice the golden ration implanted into the structure in various places.

3)Toronto’s CN Tower

The Toronto’s CN Tower, although modern, contains the golden ratio in its design. the ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of phi.  

Golden Ratio in nature

The Fibonacci Sequence or Series has a relatioship to the Golden Ratio. The Fibonacci Series shows up in the number of leaves on a plant and The Fibonaccie Wequence or Series has a relationship to the Golden Ratio.

1)The Shell

Shells are the results of a famous shape made utilizing the Golden Ratio called Golden Spirals. The Shells closely resemble this shape as seen in this picture.

Fractals in Nature

 Fractals are everywherein nature, never ending, only as far as our eyes can see. Rivers, with theirwinding channels and weird small side ones, all relatively follow the shape asthe big one, as seen in the diagram shown in class, where taking a closer lookon the small ones, show a similar shape to the main. In a video shown, therewas conclusively no way to measure the coastline, simply because having smallermeasuring equipment yield different results from larger ones. Fractals are usedto describe this coastline paradox, making it impossible to accurately measurethe actual length.

 

Favourite Fractal

My favourite fractal would have to be in trees. I find treesintriguing, just spending time to watch them sway to the wind as well as wonderhow each branch is capable to grow from the trunk, and have further branches.The leaves too, seeing the patterns on them, and being able to hold ontobranches and then just fall off.

#exploremaths

Fractals in Nature

 Fractals are everywhere
in nature, never ending, only as far as our eyes can see. Rivers, with their
winding channels and weird small side ones, all relatively follow the shape as
the big one, as seen in the diagram shown in class, where taking a closer look
on the small ones, show a similar shape to the main. In a video shown, there
was conclusively no way to measure the coastline, simply because having smaller
measuring equipment yield different results from larger ones. Fractals are used
to describe this coastline paradox, making it impossible to accurately measure
the actual length.

 

Favourite Fractal

My favourite fractal would have to be in trees. I find trees
intriguing, just spending time to watch them sway to the wind as well as wonder
how each branch is capable to grow from the trunk, and have further branches.
The leaves too, seeing the patterns on them, and being able to hold onto
branches and then just fall off.

#exploremaths

Where are Fractals in Nature?

Fractals are pretty
much just an infinite and never ending pattern where the shapes created never
end but finding one in nature may not be as hard as you think. Fractals can be
seen almost everywhere in our environment such as shorelines where they keep
splitting up into various individual rivers and the dividing branches on trees.
It’s quite intriguing how these natural occurrences can bear such a breath
taking form where it seems to be never ending.

Which Fractal is my
favourite?

Being exposed to many
fractals on Google images, it’s a tough choice to eliminate the rest and only
choose 1, however if I had to choose a fractal that I could spend my whole life
with it and it only, it would have to be the Romanesco
broccoli. It may not look like the most colourful fractal however it’s edible.
An edible fractal is all I need to make my life complete. With every mouthful
of this broccoli, its like you are consuming infinity and with that reasoning,
I don’t think any other fractal could ever be contested with the Romanesco
broccoli.

#exploremaths