Com+&+Contrast

Assignment I. Click the following link and you will find a text called "Mandelbrot and Julia Sets". Please read it carefully 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.
 * 3.5pts You can do better than this, can't you? **

**Comparisons**

//"Both Mandelbrot and Julia sets are types of fractals.// //However, these are more complicated fractals then the other fractals that have been mentioned (such as the [|Sierpinski's triangle]).// //Both these sets require the use of complex numbers.// //For the Mandelbrot and Julia sets it can be proved (through a very complex proof) that if the distance, on the Cartesian plane (remember we are using complex numbers here), between the origin and a point resulting from the iteration of some initial value is greater than 2 then the behaviour of that initial value is that it will go to infinity. If, however, after numerous iterations (possibly hundreds, thousands or more) the distance between that origin and the point is never greater than two, it is said that this point is bounded.// //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 + 0i).// //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 + 0i.// //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."//

//W//hat is quoted are the comparison, What made me notice there were comparisons was that it started mentioning that there were more fractals and it mentioned the Sierpinski's triangle, then it started pointing out characteristics about Mandelbrot and Julia sets.

**Contrasts**

//"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."//

What is quoted is the contrast, What made me notice it was a contrast is that it shows different characteristics and then it uses one example for both sets which outputs different results, showing then differences or contrasts.

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

__Triangle. It is Classified__ Triangles are classified in Scalene, Isosceles and Equilateral, t he similarity between those three is that they are geometrical shapes, they are polygons, they have three sides and three interior angles. The difference between them is the length of sides (e.g: Equilateral means all sides are equal, Isosceles means two sides are equal) and their internal angles are different. Any triangle which is in one of the three categories share S characteristics but __also have differences__ it also has differences, Equilateral triangles? have their internal angles measuring 60 degrees but the length of their sides varies from triangle to triangle: Isosceles will always have __two sides equal__ changing their length from triangle to triangle; and Scalene will only share one characteristic which is? , their sides are unequal. Talking __of the__ internal angles of triangles we can find Right, Obtuse and Acute triangles. Right triangles will always have a 90 degree angle but the other two angles can vary; Obtuse triangles will always have an angle measuring more that 90 degrees but the rest of the angles vary depending on the length of the sides; and Acute triangles have all of __it__ internal angles measuring less than 90 degrees, they depend on the length of the sides.