The Mandelbrot set is a famous example of a fractal

I. Match the words (1 –6) with their definitions/explanations (a–f):

1 similarity a without aim or purpose
2 iteration b repetition of steps to give result
3 random c say again and again; make repeatedly
4 recursion d common, seen or done every where
5 sole (criterion) e likeness
6 prevalent f one and only, single

II. Choose from (a–f) the one which best fits each of (1–5). There is one choice you do not need to use.

a. However, the term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning ‘broken" or ‘fractured’.

b. Examples of self-similar objects that are not fractals include the logarithmic spiral and straight lines, which do contain copies of themselves at increasingly small scales.

c. Images of fractals can be created using fractal-generating software

d. It involves pressing paint between two surfaces and pulling them apart.

e. Fractals can also be classified according to their self-similarity.

f. Examples include clouds, river networks, fault lines, mountain ranges, craters, snowflakes, crystals, lightning, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels, and ocean waves. DNA and heartbeat can be analyzed as fractals.


III. Work in pairs. Tell your partner about fractal.

a. Tell the definition of fractal and then where it can be found in nature.

b. Tell your partner about the types of fractals and then about fractals in artworks.


IV. On the Internet search for information about applications of fractals and then share your information with other students.

Text 13

Reading and Speaking


1. Seating in an ergonomically comfortable office chair is important for your back health. The chair’s back should not be set straight upright but angled slightly backwards to 135° in order to reduce strain on the spine and ligaments. The results of research that was conducted at Woodened Hospital in Aberdeen, Scotland was presented to the Radiological Society of North America (RSNA) on November 27, 2006 (and reported in Science Daily). It noted that the use of a ‘positional MRI’ demonstrated that a 135° back angle (while feet were resting on the floor) provided less strain and wear and tear on a back’s spine, muscles and tendons than either a 90° sitting position or sitting slouched.

Adjust your armrests for a neutral arm position or remove the arm rests if they are not useful. Always use the chair adjustment functions to create a better fit. It is important for your chair height to be set so that feet can rest on the floor. If the chair is higher, you can place your feet on a footrest.

2. Your monitor’s height is important for healthy computer work. You should be able to view the screen without having to turn your head or tilt it up or down. There is a general rule that the top of your monitor should be positioned 2’ to 3’ above your seated eye level. Decide what setting is most comfortable and doesn’t require your head to turn or tilt.

There are height adjustable desks and using an ergonomic computer workstation helps set your comfortable sitting position and monitor height.

A much easier solution is to place monitors on flexible, counterbalanced LCD monitor arms. Laptop users will benefit with a height adjustable laptop stand which can accommodate to a variety of workers and work postures.

3. Control glare. Keep the screen perpendicular to any strong light source. Use an anti-glare/anti-radiation computer filter.

4. Monitor positioning. Often, monitors are placed too close or too far away from the viewer. In both situations the computer monitor user will eventually suffer from eye strain. Depending on the size of your monitor you should center your monitor at arm’s length distance. Here again, LCD monitor arms are extremely helpful in adjusting to the most comfortable and ergonomic positioning.

5. Stable foot placement. As it was mentioned, you should adjust your chair so that your feet rest on the floor or purchase an elevated foot rest. Adjustable footrests like the ones we offer help reduce strain on back and neck muscles.

6. Organize your desk surface. Document stands eliminate desktop chaos and help you work more effectively and in maximum ergonomic comfort. Our brand name Ninka document stands can easily hold large books.

7. Proper arm and hand positioning. Your wrists should be flat and straight in relation to forearms to use keyboard/mouse/input device.

8. Eliminate the strain and twisting caused by reaching. Your arms and elbows should be relaxed and close to your body. Organizing your desk with frequently used items close by prevents you from having to reach and strain. If you are a frequent phone user, consider purchasing an ergonomic phone stand arm that swivels, frees up valuable computer desk space, and prevents you from stretching too far too often.

9. Center your equipment. Keep the monitor and the keyboard centered in front of you.

10. Negative tilt. Use a negative tilt keyboard tray with an upper mouse platform

11. Adjustable mouse platform. Or use a downward tilt-able mouse platform adjacent to keyboard.


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