Universidad Simón Bolívar. Inglés para matemáticos 1. Gerardo Cedeño. Carnet: 09-10155. Comparison & Contrast. 1) Comparison: - 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. Contrast: - 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). - 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 behavior 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. - It should be understood that these are simply the basic definitions of the two sets. The function that is iterated can be practically anything, as long as it uses complex numbers. Thus 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.
To know if something is comparison or contrast, i noticed keywords, en comparison: almost, and contrast: however and whereas.
2) Contrast: - The people use bar graphs to show of connections between two or more thing; however, if you need show the data into groups is better box plot. Comparison: - The box plots are used almost how bar graphs, but the bar graphs are more common.
5pts Great Job.
Universidad Simón Bolívar.Inglés para matemáticos 1.
Gerardo Cedeño. Carnet: 09-10155.
Comparison & Contrast.
1)
Comparison:
- 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.
Contrast:
- 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).
- 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 behavior 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.
- It should be understood that these are simply the basic definitions of the two sets. The function that is iterated can be practically anything, as long as it uses complex numbers. Thus 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.
- To know if something is comparison or contrast, i noticed keywords, en comparison: almost, and contrast: however and whereas.
2)Contrast:
- The people use bar graphs to show of connections between two or more thing; however, if you need show the data into groups is better box plot.
Comparison:
- The box plots are used almost how bar graphs, but the bar graphs are more common.