Comparison+&+contrast

** READING TO WRITE. COMPARISON AND CONTRAST. **
I.Read the text called "Mandelbrot and Julia Sets" and locate comparisons and contrasts among the fractals described there. Explain what made you notice that there were comparisons and or contrasts in the text.

** Mandelbrot and Julia Sets **
Comparison

- Both Mandelbrot and Julia sets are types of fractals. (Because it says both X and Y is the same type of thing). - Both these sets require the use of complex numbers. (Because it says the word both, too, need to use something).

Contrast

- However, these are more complicated fractals then the other fractals that have been mentioned (such as the ﻿[|Sierpinski's triangle] ﻿). (Because it emphasizes a difference between another type of fractal)

- Then, knowing that, the definition of the Mandelbrot set is: the set of all the complex numbers, c, such that the iteration of **f(z) -- > z 2 + c** is bounded (starting with z =0 + 0//i//). More simply put, the Mandelbrot set is the graph of all the complex numbers c, that do not go to infinity when iterated in **f(z) -- > z 2 + c**, with a starting value of z =0 + 0//i.//

A Julia set is almost the same thing. It is defined to be : the set of all the complex numbers, z, such that the iteration of **f(z) -- > z 2 +c** is bounded for a particular value of c. Again, more simply put it is the graph of all the complex numbers z, that do

not go to infinity when iterated in **f(z) -- > z 2 + c**, where c is constant. (Because it gives the definitions of both fractals to set differences between them)

- The basic difference between the Mandelbrot set and Julia set is that in any Mandelbrot set, you are plotting various values of c on a Cartesian plane, whereas for a Julia set, you are plotting various starting values of z, and c is kept constant. (Because it is explicitly the word difference)

II. In your own words, write the comparison and constrast of the mathematical terms you defined, described and classified.

** Polygons and polyhedrons **
Comparison

 - The polyhedrons are formed by a type of polygon that defined what we call the face of polyhedrons.  - Both are geometric figures.

Contrast

 - The polygons are plane figures while the polyhedrons are solids of three dimensions. <span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%; margin: 0cm 0cm 10pt;"> - Polygons can be circumscribed while polyhedrons don’t.