mountain ranges and coastlines all have in common?

山脈和海岸線都有共同之處？

They all contain never ending patterns known as fractals.

它們都包含著永無止境的模式，即分形。

A classic example of a fractal in nature is broccoli -

自然界中分形的一個典型例子是西蘭花------。

in that the whole stalk is a similar version of one of its branches.

以致於整個莖是其一個分支的相似版本。

So cut off one piece

那就切掉一塊

and you're left with a smaller version of the entire broccoli.

而你留下的是整個西蘭花的小版本。

Snowflakes are another example.

雪花是另一個例子。

It's often said that no two snowflakes are ever the same

人們常說，沒有兩片雪花是一樣的。

and fractals offer a fascinating explanation

和分形提供了一個迷人的解釋

as to why nature works in this way -

至於為什麼大自然會這樣運作

why nature continuously creates new, self-replicating

為什麼自然界不斷創造新的，自我複製的

yet unique structures and how the smallest things in existence

而獨特的結構，以及最小的事物是如何存在的。

are necessary components of the greater whole.

是大整體的必要組成部分。

The term fractal was coined by Benoit Mandelbrot

分形一詞是由Benoit Mandelbrot創造的。

who was working at computer giant IBM in 1980.

1980年在電腦巨頭IBM工作的他。

Mandlebrot had been fascinated by discoveries of mathematicians

曼德勒布羅特一直被數學家的發現所吸引。

from the early 19th Century

十九世紀初

who were attempting to define their understanding of what a curve is.

誰在試圖定義他們對什麼是曲線的理解。

Experiments such as Georg Cantor's discovery

喬治-康托爾的發現等實驗。

that a single line could be divided forever

一脈相承

and Helge von Koch's triangle -

和海爾格-馮-科赫的三角形--。

a shape that has an infinite perimeter but a finite area -

周長無限而面積有限的形狀------。

resulted in the term 'monsters'.

導致了 "怪物 "一詞。

Mandelbrot used the modern computing powers developed by IBM

曼德爾布羅特利用IBM公司開發的現代計算能力。

to run these monster equations millions of times over.

來運行這些怪物方程數百萬次。

This process led him to a breakthrough equation

這個過程中，他得出了一個突破性的方程。

combining the patterns found in previous monsters

結合以前的怪獸的模式

resulting in his own set of numbers.

導致他自己的一組數字。

This would become known as the Mandelbrot set -

這將被稱為曼德爾布羅特集------。

an infinite geometrical visualisation of a fractal.

分形的無限幾何可視化。

One of the most amazing things about the Mandelbrot set

曼德爾布羅特套路最神奇的地方之一是

is that theoretically, if left by itself,

是，理論上，如果離開了自己。

would continue to create infinitely new patterns

將繼續創造無限的新模式

from the original structure

原結構

proving that something could be magnified forever.

證明某件事情可以永遠放大。

Fractal geometry is currently applied in many fields.

分形幾何學目前在很多領域都有應用。

For example, research into climate change

例如，對氣候變化的研究

and the trajectory of dangerous meteorites,

和危險隕石的軌跡。

helping with cancer research

助力癌症研究

by helping to identify the growth of mutated cells.

通過幫助識別突變細胞的生長。

It's even believed by some that the universe itself may be a fractal

甚至有人認為，宇宙本身可能是一個分形體

and as you zoomed in

而當你放大後

you would discover it's made up of billions of galaxies.

你會發現它是由數十億個星系組成的。

Inside of those galaxies, you would find trillions of stars

在這些星系中，你會發現數萬億顆恆星。

and billions of solar systems and planets.

以及數十億個太陽系和行星。

And on one of those planets you would find Earth.

而在其中一個星球上，你會發現地球。

On Earth you would find continents, cities and a human.

在地球上你會發現大陸、城市和人類。

And inside of that human you would find a brain

而在那個人的身體裡，你會發現一個大腦。

made of millions of cells

細胞組成

in which you would find trillions of synapses firing away.

在其中你會發現數萬億的突觸在發射。

And inside of those you would find DNA

而在這些裡面你會發現DNA

Inside DNA you would find atoms, electrons, protons, neutrons.

在DNA裡面你會發現原子、電子、質子、中子。

Deeper still you would find quarks, neutrinos and so on

再深一點，你會發現夸克，中微子等等。

and then, just maybe, continuously deeper into infinity.

然後，只是也許，不斷深入到無限。

Some believe that, due to their highly complex and mysterious nature,

有人認為，由於其高度複雜和神祕。

the greatest use of fractals is yet to be discovered.

分形的最大用途還沒有被發現。

Thanks for watching.

謝謝你的觀看。

Don't forget to subscribe and click the bell to receive notifications for new videos.

不要忘了訂閱並點擊鈴鐺以接收新視頻的通知。

See you again soon!

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