Fractals – spinning of Infinity

26 Saturday Jul 2014

Posted by Hunt 4 Truth in Entertainment, Science, Universe

Tags

Arthur C Clark, cosmos, fractal geometry, fractal pattern, fractals, Fractals: The Colors of Infinity, Mandelbrot Set, Michael Barnsley, Physics Today, Professor Benoît Mandelbrot, Professor Ian Stewart, Scientific Illustration for the Research Scientist, Steven Hawking

How is it that there are infinities?
Since discovery of fractal geometry, infinities are everywhere. The term “fractal” was first used by mathematician Benoît Mandelbrot in 1975. A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale, it is called a self-similar pattern. As mathematical equations, fractals are usually nowhere differentiable. The mathematical roots of the idea of fractals have been traced throughout the years as a formal path of published works, starting in the 17th century with notions of recursion. The word comes fro the Latin frāctus meaning “broken” or “fractured” and fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns are found in structures and sounds, in nature, and technology.

“The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.”

~ Albert Einstein

Fractals: The Colors of Infinity
Arthur C. Clark

Video Description
Arthur C. Clarke presents this unusual documentary on the mathematical discovery of the Mandelbrot Set (M-Set) in the visually spectacular world of fractal geometry.

This show relates the science of the M-Set to nature in a way that seems to identify the hand of God in the design of the universe itself. Dr. Mandelbrot in 1980 discovered the infinitely complex geometrical shape called the Mandelbrot Set using a very simple equation with computers and graphics.

The Mandelbrot set – someone has called it the thumb-print of God – is one of the most beautiful and remarkable discoveries in the entire history of mathematics.

With Arthur C. Clarke as narrator and interviews with a number of notable mathematicians, including Benoît Mandelbrot, this program graphically illustrates how simple formulas can lead to complicated results: it explains the set, what it means, its internal consistency, and the revolutions in thought resulting from its discovery. Asked if the real universe goes on forever, Stephen Hawking defines its limit of smallness; the Mandelbrot set, on the other hand, may go on forever.

The invention of the silicon chip in the 1970′s created a revolution in computers and communication and hence transformed our way of life. We are now seeing another revolution which is going to change our view of the universe and give us a better understanding of its’ working.

The film explores the fractal universe helped by: Professor Ian Stewart of the Mathematics Institute, University of Warwick, an author of over 100 published scientific works; Dr. Michael Barnsley, former professor of mathematics at Georgia Institute of Technology who received a 2.5 million dollar government grant in 1991 to develop a fractal image compression systems.

Fractals: The Colors of Infinity
A 1995 Television Movie
The film celebrates the discovery of the Mandelbrot Set – one of the most profound and remarkable events in the history of mathematics. The programme explores the revolutionary world of Fractal Geometry – its far-reaching and often unexpected implications – its powerful and revolutionary applications.
Director: Nigel Lesmoir-Gordon
Writers: Arthur C. Clarke, Nigel Lesmoir-Gordon

Thanks for visiting.

Eric

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11 Friday Jul 2014

Posted by Hunt 4 Truth in Consciousness, Culture, Lessons, Science, Universe

≈ 4 Comments

Tags

3D printing organ, fractal geometry, fractal pattern, fractals, psychics

I always wanted to create art works that incorporate random sorts of forms like clouds for example. For most times, I was unable to do so though. This strange urge always was in the back of my mind though. Recently, I became interested in fractals because my interest in the workings of our universe led me this way. So, today, I want to share some of the basics of fractals, complex patterns and the new geometry that is necessary for physics, cosmology, biology, neuroscience, psychology, sociology, and just about every area of science and social studies.

Fractal Patterns

Fractal pattern examples include clouds, snowflakes, mountains, river networks, cauliflower or broccoli, and systems of blood vessels. Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. More examples: here and here and here

The Mandelbrot set, named after Benoit Mandelbrot, is a fractal that is infinitely complex.

Fractal Geometry

Imagine using classic geometry focused in compass and straightedge constructions to construct complex images and structures that have roughness as Benoit Mandelbrot is fond of pointing out. It’s a no-go. Trust me; I spent some time at it a few decades ago. I was able to create a work of wonder but I spent nearly a hundred hours drawing my picture with mathematical precision. Today, I would be able to set up an equation and let the computer generate my images. Here is an example of using fractal geometry to create very complex structures with roughness.

The Frax HD Fractals video is an entertaining use of fractal geometry. Now, I’ll bring us up to speed on a practical application of using fractals to meet our higher needs. Fractal geometry is useful for all sort of complex creations and these days, we are linking fractal geometry into 3D-printing technology. For example, how about medical transplants and surgeries – here is an application that may boggle your mind.

I especially love to encourage young people to get involved with exploring our latest technology and scientific areas of study. I’ve seen a lot in my years, but these days new technology and science emerge much more rapidly. I keep up with it and so can anyone. Relationships are very difficult for young people to master, whereas gaining the knowledge of complex science and technology seems unrelated, believe you me, it is directly beneficial to having success in intimate important relationships. Move quickly into school and slowly into complex relationships.

The use of fractal mathematics is revolutionizing all of the sciences. It will one day revolutionize psychology and sociology as well. Presently, I’ll stay focused on biology, medical and physics. I can see by my experience as a teacher that learning about fractals is a new foundation skill like reading and math. I’ll post more about fractals in the future, for sure. Meantime, I hope this was an interesting introduction.

Thanks for visiting; and I pay a special thanks this time to Eve, a blog friend that encouraged me to explore the frontiers of “sacred geometry” that led me to discovering the simple complexity of fractals. The images link above to Eve’s recent post about fractals. I hope you may check her pages out. I recently realized she also maintains a photography blog and she’s displayed lovely shots there. Blessing we all are to each other when we give it some time to do our best.

Eric