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]