Tag: exploremaths

When
assessment was introduced in class ideas started flowing through my head, as
the idea started feeling much easier after having to ask this one simple
question, ‘can you create this through the computer”. During these last few
weeks I’ve been gaining inspiration as I browse through the internet for more
create ideas and formulas used to create such images. After looking at some
amazing fractals including the eye straining Mandelbrot set, Julia set and the
Koch snowflake. The artwork that I will be presenting will be inspired by the
Mandelbrot set having to construct it on computer as it is just a formula and
the rest of the settings applied are by your own preference, including colour
selections, scale etc. Such fractals amazed me and I am eager to see what the
final result of my own creation can be, Furthermore I can’t wait towards
handing assessment in.

#exploremaths

Fractals are infinitely complex
patterns that are self-similar across different scales. They are created by
repeating a simple process over and over in an ongoing feedback loop. Driven by
recursion, fractals are
images of dynamic systems, what I like to call ‘the pictures of Chaos’.

Geometrically, they exist in between our familiar dimensions.
Fractal patterns are extremely familiar, since nature is full of fractals. For
example, trees, rivers, coastlines, mountains, clouds, seashells, hurricanes,
etc. Abstract fractals such as the Mandelbrot Set can be generated by a
computer calculating a simple equation over and over.

Fractals show beauty and through its state it shows nature
from a different perspective unveiling the geometrical figures and patterns,
having to portray the beauty of both nature through mathematics.

#exploremaths

As soon as this question was handed out to me, I immediately thought that this would be the only thing in Maths that I would stuff up. Fortunately, that was replaced by the idea of set theory test that was in less than a weeks time. But, after I had a look at some things on the internet of fractals in artwork, I realised that maybe I could have a tie with the test because many of the things I thought of like starting out with a rectangle then golden ratio-ing the other two parts of the rectangle were already taken by artists like the Primary golden rectangle by Marc Pouhe. So I started out with a triangle and try and make a fractal out of it somehow because what could possibly go wrong with a triangle. After having a reputation of getting a Venn Diagram named after me because of the complete utter stupidity of a 3 circle Venn Diagram, the now famously named ‘Kev-Venn Diagram, you could probably guess where my triangle went. Yep, now called a waste of paper and graphite. So, after that attempt of being the genius of triangles, I think maybe I could incorporate my artwork to a more correct version of the ‘Kev-Venn Diagram’ with some kind of fractal involved making something more correctly mathematical. #exploremaths 

#exploremaths

I was given the question of what ideas do I
have in mind for my artwork. My brain was completely blank when it came to ideas. Although
there were ideas which floated around my brain, I couldn’t figure out which one
to choose. After deliberating for a few days, I finally conjured up an idea
which I was satisfied with. The idea which I had in mind was to design an infinite
sign made out of fractals such as the Sierpinski’s triangle. The outline of my
background so far is outer space so I plan on using other shapes such as the
Apollonian gasket and tessellations to be the planets and the stars in order make
my artwork more captivating. There will also be a wide range of colours used to
illuminate my artwork for it to appear like space.

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Over the past week or so, having to think of something creative have proven to be quite difficult due to my bland personality, However after looking at some magnificent fractals online such as the eye straining Mandelbrot set and seeing such intriguing pattern with the aid of mathematics, I knew for certain that I was stuffed. Finding myself thinking about this assignment I had begun pushing my cognitive levels to extremities and ended with a half complete solution like the Kev Venn Diagram or counting half way to infinity then giving up. I would somehow incorporate fractals into my daily chores or hobbies. #exploremaths

#exploremaths

The vague structure and small amount of prompting of the assignment made my creativity feel pressured. Although I originally felt blank about what I wanted to do, I was able to gain some inspiration flipping through my exercise book. I saw Sierpinski’s triangle, the Golden Ratio, the Mandelbrot Set, and various other images. I have chosen to draw different flowers using the golden ratio. By making them different sizes and colours, I hope to create a beautiful artwork of flowers. Although I want to do this I may also incorporate other mathematical designs in the background, to make it more appealing. It is not certain that I will do that, but quite likely.

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Today in class we learnt about how the
coast line doesn’t have a definite measurement as since the coast line is not a
straight line. Therefore, we can only get an estimate of the coastline as it
will never be definite as there isn’t a scale which can measure all of the bits
and pieces of the coastline. This is known as the coastline paradox. This
relates to fractals as there are fractal-like properties in the coastline.

 

In addition to learning about the
coastline, I also learnt a lot about fractals. Fractals are infinity complex
patterns that are self-similar across different scales. This means the fractals
goes on for infinity as it keep on repeating itself. In addition to this, I also
learnt that many fractals are found in nature. Some of these places include
coastline, flowers, river networks and many more. To me, fractals are very
striking as they are not just limited to geometric patterns but can also be
used to describe the progress in time. This is very intriguing to me as it
demonstrate how fractals are more than just shapes but instead are tools in
which are very useful to the world. 

 

Favorite
Fractal

My favourite fractal was the Sierpinski
Triangle. The Sierpinski triangle was interesting to me as it not only a very
beautiful shape, but it is also very similar to the coastline. Using the
fractal, it demonstrates how the coastline cannot me measured to an exact
number. In addition to this, this fractal was my favourite because instead of
expanding out like the other fractals, it expands inwards. Furthermore, it can
be constructed as a curve of a plane, this is known as the Sierpinski’s arrow
cave.

#exploremaths

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The weekend after receiving the AT2, I had already started.
During the lesson the notification was given and we were shown 2 other pieces
done by previous students. The first, was the eye made from shapes and the
second was a circle full of circles all overlapping like a Venn diagram. This
one really caught my eye and I had decided to use a circle as the main shape
for my task.

Using the Sierpinski Triangle and various other shapes, I
hopefully have captured a beautiful piece through various things taught in
class. Originally I was going to implement golden rectangle spirals but later
decided not to.

#exploremaths

For my AT2, I have not started but I have several ideas that could be implemented onto my artwork piece. One that I have is a rectangle, resembling the golden rectangle and inside filled with endless Venn diagrams, representing both set theory and fractals and in symmetry. I would have an array of colours to help visualize the picture easier and to make it look more affectionate. I think that by having 4 main points that we have covered included into a picture would not only be beautiful in a sense (hopefully) but would also show the knowledge that I have gained from being in this class.

#exploremaths

In this lesson, I learnt about the
different types of symmetry. There are 4 types, these are rotational,
reflectional, scale symmetry and translation symmetry, also known as
tessellation. Here are two of the tessellations I found interesting.

 

Tessellation – Nature

There are a lot of tessellations that can
be found in nature, the one I found very interesting was the shell of a turtle.
The shell of a turtle is interesting as it contains more than one type of
shape. Turtle shell includes irregular hexagons surrounded by pentagons. In
addition to this, it is also enclosed with quadrilaterals. The tessellations on
the turtle’s shell is very important as without the tessellations, the shell
would easily collapse, leaving the turtle defend-less as the shell is actually
part of the turtle’s body, with it being the outgrown ribs and e vertebrae of
the turtle.

 

Tessellation – Architecture.

In addition to having tessellation found in
nature, there are also a wide range of tessellation found in architecture. An
example of this is the Federation Square in Melbourne. Federation Square is
located at the intersection between Flinders Street and Swanston Street. It was
built in 26th October 2002 and has an area of 3.2 hectares. The
outline of federation square is made out of entirely scalene triangles. The
triangles are made with the dimension 1, 2, and root 5. The triangles are then  attached together in different angles creating
interesting pattern on the building façade. Furthermore, the pinwheel tiling
pattern was used in the ‘atrium’ part of the building, which is one of the
major spaces in the federation square.

#exploremaths

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