Fractals are mathematical
formulas that are very complex. They are always repeating or making
some kind of pattern. The geometric formula is known as the Golden
Mean, Golden Ratio, or the Fibonacci Sequence. In our words fractals
are a self repeating pattern made up of different designs and get
smaller as we zoom in on them. Fractals started in the 19th
century and are growing miraculously. As you may
not know, fractals exist almost everywhere. Let us show you some
examples.
Mountains:
Simulated mountains can be one
of the most beautiful computer-operated system relevant to fractals. Math equations are used to produce the
mountains and create
life-like representations of mountains, with jags, peaks, and many
other features. Fractal mountains start off as a single, large
triangle, then break down into four smaller triangles. To make these
smaller triangles you first produce a variety of points every which
way a line crosses. Next we invent a new point from the center of
each line. Then you draw a line from one point to the next. This is
creates new triangles. Obviously, objections were made to change
points on the edges of the triangle. This produces “flat
mountains”. To make them more catching to the eye move the up and
down coordinate (y) points forward or
backward in any random amount. Large ranges of triangles will compose jagged
mountains. The range you move from each point must be separated
to make sure you don't reduce the
jaggedness. If you don't do this it won't look anything like a
mountain.
Earthquakes:
We bring to you why earthquakes can be fractals. We consider it to be
a solid on solid overlapping of Earth's crust and a plate below to
appear
to be a fractal surface. When one slides on top of another,
it gives a spark of energy that is released during a slip.
The fractals change as one slowly moves over the other. That shows
the regular amount of time of the overlapping arrangements. This
follows the law known as the Gutenberg-Richter power law which
relates to fractals.
Ocean: Oceans
can be shown as fractals through a model. There are four different
models used to show the ocean as a fractal. The first diagram is of a
regular, flat ocean. The second is a easy combination of waves to create a wave like ocean. Following the second
diagram,(the third), uses an "exponent sound function" to create the
ocean floor. Last but not least the fourth method consists of a
mathematical formula to produce waves by wind speed and under the
ocean floor.
Cauliflower: Have
you ever looked so close to cauliflower and noticed it never ended,
expanding on and on getting smaller each time? Well it's true! A
cauliflower is a fractal! Every time you zoom in closer it gets just
as unique as the whole object. Once you peel through that first layer
you see forever changing shapes drawing nearer. The tiny buds almost
seen to blossom into various designs drawing you in. Cauliflower is
definitely a fractal in many ways.
Fractal is a very
powerful word! It describes so many objects that you wouldn't occur
to even be considered fractals at first. There is no end to fractals,
they surround you every where you go. Fractals are spectacular!
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