1740 words - 7 pages

Fractals, a Mathematical Description of the World Around us

In being characterized with fractional dimensions, Fractals are considered to be a new division of math and art, which is perhaps why the common man recognizes them as nice-looking and appealing pictures that are valuable as background on computer screens and art patterns. But they are more meaningfully understood by way of the recognition that many of nature’s physical systems and a lot of human works of art are not standard geometry forms. Fractal geometry enables infinite methods of relating, evaluating and forecasting these kinds of natural phenomena. Simply said it’s a never ending pattern that repeats itself at different ...view middle of the document...

His work was revived in the 1970s by Benoit Mandelbrot who worked with IBM to show the first pictures of fractals (Patrzalek). The Mandelbrot set wasn’t discovered until 1980, this was around the time the computer came out. Was this a coincidence? No, computers made computing such math problems easier and gave us a much broader perspective on fractals. Anyone who can add and multiply can understand fractals, but such computations have to be done billions of times to make a complete set. The invention of the computer made these computations possible. This is why Mandelbrot became better associated with Benoit Mandelbrot before the previous mathematicians.

According to the Introduction of the Mandelbrot set the Mandelbrot set is a mathematical set, a collection of complex numbers. Complex numbers use a real number and an imaginary number i, for example -2+3i. The imaginary number i is used because no real number could be squared and result in a positive answer. i is equal to -1. To create the Set we pick a point C on the complex plane. The complex number corresponding with the point can be found by the equation C= a +b i, where a is the horizontal real x-axis b is the imaginary y-axis.. After calculating this expression we use the equation ￼using zero as the value of ￼ and get C for the result. Next we assign the result to and repeat the calculation. The result is the complex number . Then we have to assign the value to and repeat the process again and again. The magnitude of Z will do one of two things. It will either stay equal to or below 2 forever, or it will eventually surpass two. Once the magnitude of Z surpasses 2, it will increase forever. If the magnitude of Z eventually surpasses 2, the number is not part of the Mandelbrot set (Dewy &Patzalek).

"Fractal" is a term coined by Benoit Mandelbrot to describe an object which has a partial dimension. Students are taught in school that simple curves have a single dimension; circles, rectangles, squares polygons etc. are characterized with two dimensions and solid items such as cubes have three dimensions. It is known that these three aspects describe space. Usually dimensions are better understood in terms of integers such as 1, 2, 3, 4, …. The most distinctive feature of fractals is that they are characterized with fractional dimensions. For instance, a fractal curve can be having a dimensionality of 1.3243, instead of just 1. It is noteworthy that fractals cannot be considered as only mathematical inquisitiveness because it has been proved that most natural items are naturally fractal and are best defined through the use of fractal mathematics. Mandelbrot made the quote “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 famous (Patrzalek).” This puzzled many math mathematicians because if you can’t define...

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