Fractal continuum. Not the one from Final Fantasy.

fractal, spiral, art
Photo by alto2 on Pixabay

The longing for the meaning of life resonates deep within each of us. We believe that our lives have sense. We long to make a difference in the world, but life is chaotic and unpredictable. Often, despite our best efforts to make a difference, we fail to do so.

Fractal geometry consists of a basic original simple shape/pattern that is duplicated repeatedly, thus increasing in complexity. If we change the original simple pattern, we change all the other generations of shapes.

The paradox of chaos and order exists in every area of life. Fractals show how chaos and order work together. They create beauty out of simplicity. The destructive energy of chaos creates a space for change that allows us to know ourselves better, to become stronger. It forces us to discover our potential, the meaning of life. It teaches us how to find new ways with clarity of purpose, evolve freely, and create amazing things even in difficult situations. To live passionately and thrive.

Fractal geometry has succeeded in capturing a different kind of beauty than the perfect beauty of the ideal shapes of classical geometry. The beauty of fractals lies in the delicate harmony between regularity and randomness. In this harmony also lies the beauty of nature.

Nature blesses us with an infinite number of fractals in the winter season in the form of beautiful but cold white clumps. It is a time when nature slows down its cycle and gains new strength for another beginning. We, too, if we want to make a life change that is meant to bring us closer to ourselves, must first slow down, withdraw from the routine, and tune in to our true selves. This will help us recharge for new beginnings.

We can observe fractals in rainforests, in modern medical research, in movies, and all over the world in wireless communication networks. Yet, the greatest secret of natural design is a strange-looking shape that we may never have heard of but is all around us. A curvilinear repeating form called a fractal. Fractals are in our lungs, kidneys, blood vessels, but also in flowers, plants, the climate system, the rhythm of the heart, the very essence of life.

Figuring out how they work, however, required mathematics. A mathematician who would deal with the old preconceptions about the strange forms of nature. His name was Benoit Mandelbrot. He didn’t work with equations; he worked with images; he had done it all his life. He could see things that no one else had predicted until he pointed them out. He claimed that many natural shapes could be described mathematically by fractals. He used this word to describe skeletal shapes. He made it possible for people to see forms that were always around them but seemingly invisible. The invisible suddenly became visible. Order appeared in the chaos.

Mandelbrot argued that he could create a fractal from a simple shape if he repeatedly broke it into smaller pieces. Loren Carpenter decided to test this theory in computer graphics. In 3 days, he managed to create mountain ranges. The method was simple. You start with a landscape made of large triangles. Then you divide each one into four more triangles. This is repeated over and over again. Mathematicians call it interaction. It’s the basis of fractal geometry.

The images that were computer-generated in this way were breathtaking. This opened up a whole new world for animation. Carpenter used this method to create the planet in Star Trek II and Evans & Sutherland and later George Lucas also built on this method. Startrek II was the first feature film with scenes entirely created with computer graphics.

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