Unit 1: Fractals
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
Benoît Mandelbrot , “The Fractal Geometry of Nature”
If you like fractals, it is because you are made of them. If you can’t stand fractals, it’s because you can’t stand yourself. It happens. Homer Smith
WARM-UP
Work in pairs. Look at the pictures below. What do you think they have in common? Note down your ideas and share them with other students.
traditional patterns from Africa
cloud formations seen from space
broccoli
the cells inside the woody stalk of a plant
A. What comes into your mind when you hear the word ‘fractals’? Read the definition of a fractal below. What fractals do you know or can you think of?
A fractal is a geometric entity whose basic patterns are repeated at ever decreasing sizes.
B. Think of three things you would like to know about fractals, and write them down.
Do
you support the ideas that fractal geometry is
the true geometry of Nature whereas Euclidian geometry is concerned
with abstract perfection almost non-existent in nature?Have you heard of the chaos theory? Do you think natural systems’ behavior possesses some kind of subtle order?
A. Discuss the quotations in pairs.
“Fractal geometry is not just a chapter of mathematics, but one that helps everyman to see the same world differently.” Benoit Mandelbrot
“I find the ideas in the fractals, both as a body of knowledge and as a metaphor, an incredibly important way of looking at the world.” Al Gore
“Much of life is designed in a fractal-like way.” Jim Brown
B. Do you agree with Yannick Joye who has said of fractals “… as a result of evolution, the brain has a preference for fractal structures, and feels relaxed when surrounded by these …” ? Do you like looking at fractal patterns?
READING
Identify the stressed sound in each word as in the example.
rough, miniature, feedback, recursion, iteration, deterministic, entire, recurrence, coastline, astrophysics, architecture, economics, mosaic, segmented, similarity
Put the following words into the corresponding column according to the sound of the adjective or regular past ‘ed’.
fragmented, traced, coined, based, analyzed, classified, defined, iterated, distorted, preserved, considered, segmented, applied, used, described
/t/ |
/d/ |
/id/ |
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Some sentences have been removed from the text by mistake. Read the text below and put each sentence into its appropriate place in the text.
Most natural objects, when analyzed in two dimensions, rank between 1.2 and 1.6.
The list of known physical fractal systems is long and growing rapidly.
However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.
Two of the most popular types of fractals are complex number fractals and Iterated Function System (IFS) fractals.
Two of the most important properties of fractals are self-similarity and non-integer dimension.
They tap into a central quality of nature – the fractured pieces which yet make her whole.