Put the words in brackets into the correct form.

Brownian 1) … (move) of particles, the ups and downs of the stock market, the spread of epidemics as well as the 2) … (destroy) paths of forest fires are all examples of 3) … (chaotic) in nature, with invisible, fractal order lurking underneath.

In the past 10 to 20 years, researchers in psychology have been finding 4) …. (increase) examples of fractal patterns across each of the domains of psychology including 5) … (intend) behaviors, 6) … (vision) search, and speech patterns.

Fractal dynamics afford language its 7) … (remark) flexibility – the ability for a limited number of words and grammatical rules to enjoy unlimited 8) … (combine).

Fractal analysis, the 9) … (model) of data by fractals, consists of methods to assign a fractal dimension and other fractal 10) … (characterize) to a signal, dataset or object which may be sound, images, molecules, networks or other data.

One of the underlined parts of a sentence contains a mistake. Find it and correct.

Fractal geometry had permeated many areas of science, such as astrophysics, biological sciences, and has become one of the most important techniques in computer graphics.

Although fractal geometry is closely connected with computer techniques, some people had worked on fractals long after the invention of computers.

Both chemically-formed crystals and ice and frost crystals are breathtaking examples of fractals nature.

As fractal surfaces in three dimension Euclidean space, mountains typically have dimensions around 2.2.

Mandelbrot's fractal geometry replaces Euclidian geometry which is dominating our mathematical thinking for thousands of years.

If a hurricane is a chaotic system, then the wreckage strewn in its path is it fractal pattern.

Nowadays, computer-generating fractal art, and the software to generate it, are widely available on the Internet.

A simple mathematical formula: z -> z^2 + c now named after its inventor and is called the Mandelbrot set.

Nobody really knows how many stars actually glitter in our skies, but did you ever wonder how they were formed and ultimately found their home in the Universe?

It was Mandelbrot, for instance, who when investigating economics first discovered that seemingly random market price fluctuations can be followed a hidden mathematical order over time.

Rewrite the sentences using the passive voice where possible. Omit the agent where it can be omitted.

Radio waves have carried a man's voice to Earth from the surface of the moon, but gamma rays can fatally damage our DNA.

Who wrote "One Hundred Years of Solitude?"

Do they pay their workers on time?

They heard her complaining about the new timetable.

You should have booked the tickets weeks ago.

They are going to give him a promotion.

Fractals will always attract human beings.

Before the development of fractal geometry, scientists regarded Nature as noisy Euclidean geometry.

The Italian mathematician Guiseppe Peano first proposed the most famous of space-filling curves in 1890.

Architects use the typical measurement techniques of fractal geometry to analyse the structure of buildings.

Trees and ferns are fractal in nature and we can model them on a computer by using a recursive algorithm.

People are cutting down rainforests in the Amazon.

We can produce many beautiful designs that resemble natural patterns using the Koch recursion.