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Learning resources from INTO UEA

Mandelbrot

Watch the video and write down the words you hear that have similar meanings to the words below. For example, the first word in the list is prescribes. You hear the word defines. Write this word down.

  1. prescribes = defines
  2. soft =
    fluffy
  3. collective =
    common
  4. almost =
    nearly
  5. decreasing =
    smaller and smaller
  6. split =
    fork
  7. repeatedly =
    over and over (again)
  8. in every part of =
    throughout
  9. formed =
    made up
  10. completely =
    entirely
  11. express =
    represent
  12. most important part =
    essence
  13. artificial =
    man-made
  14. unbelievable =
    incredible
  15. equipped =
    armed
  16. identifying mark =
    thumbprint

Watch the video, complete the gaps on a piece of paper, then check your answers.

Mandelbrot asks if there’s something
unique
that defines all the
varied
shapes in nature. Do the fluffy surfaces of clouds, the branches in trees and rivers, the crinkled
edges
of shorelines share a common mathematical
feature
? Well, they do.
Underlying
nearly all the shapes in the natural world is a mathematical
principle
known as self-
similarity
. This describes anything in which the same shape is repeated over and over again at smaller and smaller
scales
.
A great example are the branches of trees. They fork and fork again, repeating that simple
process
over and over at smaller and smaller scales. The same branching principle applies in the
structure
of our lungs and the way our blood vessels are
distributed
throughout our bodies. It even describes how rivers split into ever smaller streams. And nature can repeat all sorts of shapes in this way. Look at this Romanesco broccoli. Its
overall
structure is made up of a
series
of repeating
cones
at smaller and smaller scales. Mandelbrot realized self-similarity was the
basis
of an entirely new kind of geometry and he even gave it a name: fractal.
Now that’s a pretty neat
observation
. But what if you could represent this
property
of nature in mathematics? What if you could
capture
its essence to draw a picture? What would that picture look like? Could you use a simple set of mathematical
rules
to draw an
image
that didn’t look man-made?
The answer would come from Mandelbrot, who had taken a
job
at IBM in the late 1950s to gain
access
to its incredible computing power and
pursue
his obsession with the mathematics of nature. Armed with a new breed of supercomputer, he began
investigating
a rather curious and strangely simple-looking
equation
that could be used to draw a very unusual shape.
What I’m about to show you is one of the most remarkable mathematical images ever
discovered
. "Epic" doesn’t really do it justice. This is the Mandelbrot set. It’s been called the thumbprint of God.

Mandelbrot asks if there’s something unique that defines all the varied shapes in nature. Do the fluffy surfaces of clouds, the branches in trees and rivers, the crinkled edges of shorelines share a common mathematical feature? Well, they do. Underlying nearly all the shapes in the natural world is a mathematical principle known as self-similarity. This describes anything in which the same shape is repeated over and over again at smaller and smaller scales.

A great example are the branches of trees. They fork and fork again, repeating that simple process over and over at smaller and smaller scales. The same branching principle applies in the structure of our lungs and the way our blood vessels are distributed throughout our bodies. It even describes how rivers split into ever smaller streams. And nature can repeat all sorts of shapes in this way. Look at this Romanesco broccoli. Its overall structure is made up of a series of repeating cones at smaller and smaller scales. Mandelbrot realized self-similarity was the basis of an entirely new kind of geometry and he even gave it a name: fractal.

Now that’s a pretty neat observation. But what if you could represent this property of nature in mathematics? What if you could capture its essence to draw a picture? What would that picture look like? Could you use a simple set of mathematical rules to draw an image that didn’t look man-made?

The answer would come from Mandelbrot, who had taken a job at IBM in the late 1950s to gain access to its incredible computing power and pursue his obsession with the mathematics of nature. Armed with a new breed of supercomputer, he began investigating a rather curious and strangely simple-looking equation that could be used to draw a very unusual shape.

What I’m about to show you is one of the most remarkable mathematical images ever discovered. "Epic" doesn’t really do it justice. This is the Mandelbrot set. It’s been called the thumbprint of God.