Fractal mito

From conch and spiral nebula to human lung structure, we are surrounded by various chaotic patterns.

Fractal (a geometric shape that is repeatedly folded at smaller and smaller scales, resulting in nonstandard shapes and surfaces that cannot be defined by standard geometry) is composed of chaotic equations, including self-similar patterns, which will become more and more complicated by amplification.

If a fractal pattern is divided into several parts, the result will be a replica with a reduced size but the same shape as the whole pattern.

The mathematical beauty of fractal is to form infinitely complex patterns with relatively simple equations. It forms beautiful patterns by repeating the fractal generation equation many times.

We have collected some natural examples of this on the earth. Let me have a look.

1. Broccoli: It has a golden spiral.

This cauliflower is the most important fractal vegetable. Its pattern is a natural representation of Fibonacci sequence, or golden spiral (a logarithmic spiral with the center of the flower ball as the symmetry axis and the small flowers arranged in a spiral).

2. The world's largest salt marsh-the mirror of the sky

salt marsh

The hard salt layer presents a very consistent irregular pattern.

In the last century, the San Francisco Bay Salt Marsh pictured above has been used for industrial salt production.

The picture below shows the Uyuni salt marsh, the largest salt marsh in the world in southern Bolivia. The hard salt layer presents a very consistent irregular pattern, which is a typical fractal.

3, ammonite suture

The ammonite, extinct about 65 million years ago, is a marine cephalopod that divides the spiral shell into many compartments.

The shell wall between these spaces is called suture, which is a fractal complex curve.

Stephen jay gould, a famous American paleontologist, concluded from the complexity of ammonite sutures in different periods that evolution has not driven them to become more complicated, and we humans are obviously "an exception" and unique in the universe.

The shell of ammonite also grows into a logarithmic spiral shape. Obviously, this pattern often appears in nature, such as Roman cauliflower.

4. Mountains

Mountains are the same product of tectonic force and erosion. Tectonic forces promote crustal uplift, and erosion leads to partial crustal subsidence. The product of the interaction of these factors is fractal.

The picture above shows the Himalayas, which is home to many of the highest peaks in the world. The Indian plate collided with the Eurasian plate about 70 million years ago, which led to the uplift of the Himalayas, and the height of this mountain is still increasing.

5.ferns

Pteridophytes are a common self-similar pattern, which means that their patterns can be generated and replicated at any magnification or reduction rate.

The mathematical formula for describing ferns is named after michael barnes, who was the first to show that this chaotic state is unpredictable and generally follows the deterministic law (based on the nonlinear cyclic equation).

That is to say, barnsley's fernlike formula is used to repeatedly generate any number, and finally a unique fernlike object is generated.

6. Cloud

The layered cloud above was photographed by Aka satellite over the South Pacific Ocean near the west coast of Africa. Fractal cloud pattern separated by a series of twill clouds.

According to NASA's Earth Observatory, it is rare to see such a clear dividing line in such a continuous cloud, and scientists have failed to explain how it formed.

According to NASA, a series of 200-mile (32 1.87 km) vortex clouds may be the longest such clouds photographed so far.

These clouds are also called von Kármán cloud streets, named after the late fluid dynamicist Theodore von Kármán. When low-altitude clouds are interrupted by objects such as islands, cloud streets will be formed. The wind under the wing sometimes forms this pattern.