What Is a Fractal?

A fractal is a geometric figure whose parts have the same statistical character as its whole.

Fractals are found everywhere in nature, as deep as the nano-scale, and as profound as the universe-scale.

The beauty of this design lies within the fact that it mixes art, geometry, alchemy, physics, and biology to give life an equation that could be easily found at every scale of it!

Image result for fractal graphic design gif

What Defines a Fractal?

The 2 most important properties of fractals are:

1. Self-Similarity

Just like in a fern, the self-similarity held within a fractal is observed no matter how much you zoom in into the structure. The same pattern will undoubtedly appear with each magnification step!

Image result for fractal fern

2. Non-Integer Dimension

Classical geometry describes objects with integer dimensions: 0-dimensional points, 1-dimensional lines and curves, 2-dimensional planes, and 3-dimensional solids.

Image result for non-integer dimension

However, natural phenomena are better described using a dimension that lies between two integers, and hence the name “non-integer”.

So, the more the flat fractal fills a plane, the closer it approaches 2-dimensions. While the more it is composed of medium-sized hills, the closer it is to 3-dimensions.

Math Alert! Below is the formula of how dimensions are calculated:

Image result for non-integer fractal dimension

Image result for non-integer fractal dimension

Fractals: From Atoms to the Universe

Atoms

neutron1.jpg
Atomic Model
8199dfaf01442383f7c8b3c6353f9ed7.jpg
Atoms of a Crystal

DNA

Related image
DNA Bonds
Image result for DNA fractal
DNA Scheme

Cells

Image result for cells under microscope
Grass Cells
Related image
Starfish Cells
Related image
Cancer Cells
Image result for cells under microscope
Green Leaf Cells
Image result for fractals in cells
Brain Cells
Related image
Choroid Plexus Cells

Organs

Image result for brain fractals
Brain
Related image
Blood Vessels
Related image
Eye

Nature

Image result for fractals in trees
Trees
Related image
Sea Urchin
Related image
Sun Flower
Related image
Lily Pad
Related image
Butterfly
Related image
Leopard
Related image
Snowflakes
Image result for cloud fractals
Clouds
Image result for lightening
Lightening

Space

Related image
Andromeda Galaxy
Related image
Star Clusters
Related image
Helix Nebula

As above, so below.

As within, so without.

As the universe, so the soul.

Everything in nature is connected to everything, and everything resembles everything in a very simple-complex manner!

We are merely parts of a whole, an intricate design…

Food for thought?!

Check our coming posts for more beautiful details about fractals!

References:

http://www.fractal.org/Bewustzijns-Besturings-Model/Fractals-Useful-Beauty.htm

http://www.crystalinks.com/fractals.html

Ranim Daw & Rafik Chbaklo

R-Health Formula

March 29, 2017

Advertisements