29. Prepare a short two-minute presentation for your classmates on one of the topics below. You may use the information from the unit or do some research on the Internet.

• History of fractals

• Types of fractals (the Cantor set, Julia sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve. the Lyapunov fractal etc.)

• Emotional influence of fractal patterns on humans

• Fractals in art and / or architecture

• Application of fractal analysis

• Fractal antennas

• Natural fractals

• Properties of fractals

• The drip-paintings of Jackson Pollock

• Benoit Mandelbrot

30. Comment on the cartoon by David Shrigley.

31. Explain what the following branches of science study.

Astrophysics, meteorology, seismology, enzymology, biology, finance.

32. Look at the examples of fractals in art. The first is a drip-painting of Jackson Pollock "Number 8," 1949; the second (by Mark J. Brady) and the third (author unknown) are computer-generated. Which of the pictures do you like more? Why?

    1

    2

    3

33. Work in pairs. You are going to read about fractal patterns in the quantum world and biological sciences (Further Reading, UNIT 1). Student A reads the text “Fractal patterns spotted in the quantum realm”, Student B reads about fractals in the biological sciences. Make notes and retell the text to your partner.

34. You've read some interesting information about one of the scientists who made a great contribution into the study of fractals. Share this information with your classmates.

LISTENING

35. You are going to listen to some information about psychological influence of fractal patterns on humans. Before you listen, check if you know the meaning of the following words and phrases:

crucial implications, stress-induced, schizophrenia, canvas, tessellations, biophilic, soothing, to be hard-wired

36. Decide whether the facts from the text are true or false.

1. Looking at fractals causes positive physiological changes in people.

2. During their experiments the researchers measured the levels of brain activity.

3. Study shows that fractals reduce stress level by 16%.

4. Stress-reduction leads to physiological resonance.

5. Stress is one of the reasons of schizophrenia.

6. In future, researchers want to incorporate stress-reducing fractals into our surrounding environment.

1	2	3	4	5	6

37. Listen again and complete the phrases.

1. to examine how people _________

2. a specific form of fractal found ___________

3. the fractal structure ____________

4. exposure to fractals automatically _____________

5. surrounds itself with ______________

6. people’s responses to _______________

7. to collaborate with artists _____________

8. explain their enduring ______________

38. Write down two potential applications of “biophilic” fractals mentioned in the text.

WRITING

39. Choose any 3 verbs from the list and use them in your own sentences. The verbs should be in the passive form.

To split, to break, to fill, to give, to distort, to display, to preserve, to find.

40. Choose one of the statements and write your comments (70 -80 words).

• “No one is considered scientifically literate today who does not know what a Gaussian distribution is or the meaning and scope of the concept of entropy. It is possible to believe that no one will be considered scientifically literate tomorrow who is not equally familiar with fractals.” the American physicist John A. Wheeler

• Math prided itself in its detached, abstract isolation, completely apart from the real world - particularly nature - breathing instead the refined and pure air of its own self-contained universe of number. In the last century it even divorced itself from physics, its sister science for centuries.