What Is A Fractal (and what are they good for)? - By MITK12Videos
Transcript
| 00:01 | every science hold . What does snowflakes and cell phones | |
| 00:08 | have in common ? The answer is never ending patterns | |
| 00:11 | called fractals . Let me draw a snowflake . I'll | |
| 00:15 | start with an equilateral triangle , then I'll draw another | |
| 00:18 | equilateral triangle on the middle of each side , pull | |
| 00:22 | out the middle and repeat the process this time with | |
| 00:25 | 1234 times three , which is 12 sides . If | |
| 00:29 | I do this over and over , the shape will | |
| 00:32 | look something like this . This is called a coke | |
| 00:35 | snowflake and it has a special property , no matter | |
| 00:38 | where I look or how much I zoom in , | |
| 00:39 | I will see the same pattern over and over . | |
| 00:42 | Never ending patterns like this . That on any scale | |
| 00:45 | on any level of zoom , look roughly the same | |
| 00:47 | or called fractals . We can actually draw a coke | |
| 00:50 | snowflake on the computer by having it repeatedly graph a | |
| 00:54 | mathematical equation . Each time we had a triangle , | |
| 00:57 | one side of the coke . Snowflake will turn into | |
| 00:59 | four . After the first repetition , will get three | |
| 01:02 | times four to the first , or 12 sides after | |
| 01:06 | the second repetition , will get three times four to | |
| 01:08 | the second , or 48 sides after repetition number and | |
| 01:13 | we'll have three times four to the end sides . | |
| 01:16 | If we do this , an infinite number of times | |
| 01:18 | will get infinitely many sides . So the perimeter of | |
| 01:21 | the Koch , snowflake will be infinite . But the | |
| 01:24 | area of the coke snowflake wouldn't be infinite . If | |
| 01:27 | I draw a circle with a finite area around the | |
| 01:30 | snowflake , it will fit completely inside , no matter | |
| 01:33 | how many times we increase the number of sites . | |
| 01:36 | So the coke fractal has an infinite perimeter but a | |
| 01:40 | finite area . In the 19 nineties , a radio | |
| 01:44 | astronomer named Nathan Cohen used the fractal antenna to rethink | |
| 01:48 | wireless communications At the time , Cohen's landlord wouldn't let | |
| 01:53 | him put a radio antenna on his roof . So | |
| 01:55 | Cohen decided to make a more compact , fractal like | |
| 01:58 | radio antenna instead , but it didn't just hide the | |
| 02:02 | antenna from his landlord . It also seemed to work | |
| 02:04 | better than the regular ones . Regular antennas have to | |
| 02:07 | be cut for one type of signal and they usually | |
| 02:10 | work best when they're lengths a certain multiples of their | |
| 02:12 | signals wavelength . So FM radio antennas can only pick | |
| 02:15 | up FM radio stations , tv antennas can only pick | |
| 02:18 | up tv channels and so on . But fractal antennas | |
| 02:22 | are different as the fractal repeats itself more and more | |
| 02:25 | . The fractal antenna can pick up more and more | |
| 02:27 | signals , not just one and because the perimeter of | |
| 02:30 | the Koch snowflake grows way faster than its area , | |
| 02:32 | the fractal antenna only takes up a quarter of the | |
| 02:35 | usual space , but Cohen didn't stop there . He | |
| 02:38 | designed a new antenna this time using a fractal called | |
| 02:41 | the Mentor sponge . The Mentor sponges kind of like | |
| 02:44 | a three D . Version of the coke snowflake . | |
| 02:46 | It has infinite surface area but finite volume . Mentor | |
| 02:50 | sponges . Sometimes used in cell phone antennas , it | |
| 02:53 | can receive all kinds of signals while taking up even | |
| 02:56 | less area than a coke snowflake . Now these antennas | |
| 02:59 | aren't perfect . There are smaller , but they're also | |
| 03:02 | very intricate , so there are harder and more expensive | |
| 03:04 | to make and although fractal antennas can receive many different | |
| 03:08 | types of signals , they can always receive each signal | |
| 03:11 | as well as an antenna that was cut for it | |
| 03:14 | . Cohen's invention was not the first application of fractals | |
| 03:17 | . Nature has been doing it forever and not just | |
| 03:20 | with snowflakes . You can see fractals and river systems | |
| 03:23 | , lightning bowls , seashells and even whole Galaxies . | |
| 03:27 | So many natural systems previously thought off limits to mathematicians | |
| 03:31 | cannot be explained in terms of fractals and by applying | |
| 03:34 | nature's best practices , we can then solve real world | |
| 03:37 | problems . Factor research is changing fields such as biology | |
| 03:41 | , for example , 20 scientists discovered the chroma tin | |
| 03:45 | is a fractal and that keeps DNA from getting tangled | |
| 03:48 | . Look around you . What beautiful patterns do you | |
| 03:52 | see ? Yeah . Hi , I'm Julia . Thanks | |
| 03:57 | for watching . Science allowed . Check out these other | |
| 03:59 | awesome videos and visit our website . Yeah . |
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