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  • What do galaxies, cloud formations, your nervous system,

    星系、雲層、你的神經系統是什麼。

  • 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!

    再見

What do galaxies, cloud formations, your nervous system,

星系、雲層、你的神經系統是什麼。

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