1 00:00:00,500 --> 00:00:05,620 What do snowflakes and cell phones have in common? 2 00:00:05,620 --> 00:00:10,250 The answer is never-ending patterns called fractals. 3 00:00:10,250 --> 00:00:14,690 To explain, let me start by drawing a snowflake. 4 00:00:14,690 --> 00:00:17,460 First I draw an equilateral triangle, 5 00:00:17,460 --> 00:00:20,280 divide each side into three parts, 6 00:00:20,280 --> 00:00:24,880 and draw another equilateral triangle on top of each one. 7 00:00:24,880 --> 00:00:27,920 Then take out the middle and repeat the process, 8 00:00:27,920 --> 00:00:30,780 this time with one, two, three, four times 9 00:00:30,780 --> 00:00:32,910 three, which is 12 sides. 10 00:00:32,910 --> 00:00:36,230 Eventually, the shape will start looking something like this. 11 00:00:36,230 --> 00:00:39,280 In mathematics, this is called a Koch snowflake. 12 00:00:39,280 --> 00:00:42,100 If I repeated my process again and again, 13 00:00:42,100 --> 00:00:46,090 I would see this same pattern anywhere I looked. 14 00:00:46,090 --> 00:00:49,710 This is a Koch snowflake, this time drawn on a computer. 15 00:00:49,710 --> 00:00:52,290 Such never-ending patterns that on any scale, 16 00:00:52,290 --> 00:00:54,330 on any level of zoom, look roughly the same, 17 00:00:54,330 --> 00:00:56,050 are called fractals. 18 00:00:56,050 --> 00:00:58,940 Computer scientists can program these patterns 19 00:00:58,940 --> 00:01:01,550 by repeating an often simple mathematical process 20 00:01:01,550 --> 00:01:03,050 over and over. 21 00:01:03,050 --> 00:01:07,560 In the 1990s, a radio astronomer by the name of Nathan Cohen 22 00:01:07,560 --> 00:01:11,810 used fractals to revolutionize wireless communications. 23 00:01:11,810 --> 00:01:15,090 At the time, Cohen was having troubles with his landlord. 24 00:01:15,090 --> 00:01:17,520 The man wouldn't let him put an antenna on his roof. 25 00:01:17,520 --> 00:01:23,100 So Cohen designed a more compact fractal radio antenna instead. 26 00:01:23,100 --> 00:01:26,080 The landlord didn't notice it, and it worked better 27 00:01:26,080 --> 00:01:27,770 than the ones before. 28 00:01:27,770 --> 00:01:31,270 Working further, Cohen designed a new antenna, 29 00:01:31,270 --> 00:01:35,720 this time using a fractal called the Menger sponge. 30 00:01:35,720 --> 00:01:37,820 The Menger sponge is not really the sponge 31 00:01:37,820 --> 00:01:39,460 you'd be scrubbing your back with, 32 00:01:39,460 --> 00:01:41,350 but you can still think of it like that. 33 00:01:41,350 --> 00:01:44,180 Imagine both water and soap getting through your sponge's 34 00:01:44,180 --> 00:01:47,880 holes, except the water is Wi-Fi and the soap is, 35 00:01:47,880 --> 00:01:49,415 say, Bluetooth. 36 00:01:49,415 --> 00:01:51,450 The fractal's infinite sponginess 37 00:01:51,450 --> 00:01:54,000 allows it to receive many different frequencies 38 00:01:54,000 --> 00:01:55,310 simultaneously. 39 00:01:55,310 --> 00:01:57,460 Before Cohen's invention, antennas 40 00:01:57,460 --> 00:02:00,700 had to be cut for one frequency and that was the only frequency 41 00:02:00,700 --> 00:02:01,980 they could operate at. 42 00:02:01,980 --> 00:02:04,170 Without Cohen's sponge, your cell phone 43 00:02:04,170 --> 00:02:06,400 would have to look something like a hedgehog 44 00:02:06,400 --> 00:02:09,160 to receive multiple signals, including 45 00:02:09,160 --> 00:02:11,890 the one your friends use when they call. 46 00:02:11,890 --> 00:02:14,240 Cohen later proved that only fractal shapes 47 00:02:14,240 --> 00:02:16,570 could work with such a wide range of frequencies. 48 00:02:16,570 --> 00:02:19,130 Today, millions of wireless devices, 49 00:02:19,130 --> 00:02:21,480 such as laptops and barcode scanners, 50 00:02:21,480 --> 00:02:24,160 use Cohen's fractal antenna. 51 00:02:24,160 --> 00:02:26,200 Cohen's genius invention, however, 52 00:02:26,200 --> 00:02:29,010 was not the first application of fractals in the world. 53 00:02:29,010 --> 00:02:31,460 Nature has been doing it the whole time, and not 54 00:02:31,460 --> 00:02:32,620 just with snowflakes. 55 00:02:32,620 --> 00:02:35,420 Natural selection favors the most efficient systems 56 00:02:35,420 --> 00:02:37,940 and organisms, often of a fractal form. 57 00:02:37,940 --> 00:02:39,620 The spiral fractal, for example, is 58 00:02:39,620 --> 00:02:43,160 present in sea shells, broccoli, and hurricanes. 59 00:02:43,160 --> 00:02:45,730 The fractal tree is relatively easy to program 60 00:02:45,730 --> 00:02:49,010 and can be used to study river systems, blood vessels 61 00:02:49,010 --> 00:02:50,710 and lightning bolts. 62 00:02:50,710 --> 00:02:52,440 So many natural systems previously 63 00:02:52,440 --> 00:02:54,670 thought off-limits to mathematicians 64 00:02:54,670 --> 00:02:57,720 can now be understood in terms of fractals. 65 00:02:57,720 --> 00:03:01,060 Mathematics allows us to learn nature's best practices 66 00:03:01,060 --> 00:03:04,270 and then apply them to solve real-world problems. 67 00:03:04,270 --> 00:03:06,950 Much like Cohen's antenna revolutionized 68 00:03:06,950 --> 00:03:09,500 telecommunications, other fractal research 69 00:03:09,500 --> 00:03:13,300 is changing medicine, weather prediction and art, 70 00:03:13,300 --> 00:03:16,750 here at MIT and everywhere in the world. 71 00:03:16,750 --> 00:03:17,830 Look around you. 72 00:03:17,830 --> 00:03:19,880 What beautiful patterns do you see? 73 00:03:19,880 --> 00:03:23,230 [JAZZ MUSIC]