The fun filled fractal phenome Essay Example For Students

The fun filled fractal phenome Essay The Fun Filled Fractal PhenomenonA fractal is a type of geometric figure. It is generated by starting with a very simple pattern such as a triangle and, through the application of many repeated rules, adding to the figure to make it more complicated. Often, an input will be entered into a recursive function and it will yield an output. This output is then inserted back into the function as an input and the process is repeated infinitely. Fractals often exhibit self-similarity. This means that each small section of the fractal can be viewed as a reduced-scale replica of the whole. Some famous fractals include Sierpinskis triangle, Kochs snowflake and the length of a coastline. Fractals were brought to the publics attention by the work of French mathematician Benoit B. Mandelbrot in the 1970s. Mandelbrot discovered how to calculate fractal dimensions. The formula for fractal dimension is N=2D where N equals the number of copies of the original figure, which is calculated by doubling it s size and D is the dimension. Mandelbrot named his creations fractals because each part is a fraction of the whole figure. The Chaos Theory describes the complex and unpredictable motion of systems that are sensitive to their initial conditions. Chaotic systems follow precise laws but their irregular behavior can appear to be random to the casual observer. For example, weather is a chaotic system. If the rays of the sun bounce off the hood of a car in a certain way, causing a breeze, the breeze could blow a leave off a tree, which starts a series of additional events that could alter the weather in some other part of the world. Chaos can be related to fractals. In a fractal if one tiny change occurs in a repeated pattern, the entire fractal will change. The above picture is an example of a strange attractor that charts the trajectory of a system in chaotic motion. It is a fractal. The fractal exhibiting chaos is predictably unpredictable. This is because, in a chaotic system, it is predictable that there will be minute changes that will alter the entire shape. We will write a custom essay on The fun filled fractal phenome specifically for you for only $16.38 $13.9/page Order now Kochs snowflake, (above ) exhibits the concept of an infinite perimeter with a finite area. Kochs snowflake is created by dividing each of the sides of an equilateral triangle into three equal parts. Next, the center part of each side is taken out and replaced with two sides of equal length to that of the original centerpiece. This pattern is repeated infinitely. Each time the process is completed the perimeter gradually increases to infinity by increments of 4/3. However, the area of this snowflake is finite. If you draw a circle enclosing the original triangle that contains the vertices of the triangle, the area of the snowflake will never exceed the area of that circle no matter how many times its perimeter increases. Therefore, it has a finite area. Fractals exhibit self-similarity. This is the concept that each small portion of the fractal can be viewed as a reduced-scale replica of the whole. For example, in Sierpinskis Triangle, each small triangle inside is similar to the lar ge one on the outside. A real life example of self-similarity is a tree. The tree has a trunk on which limbs grow. Branches grow from the limbs, and twigs grow from the branches, which is followed by sticks on the twigs and so on. The sticks growing on the twigs are just a smaller version of the twigs growing on the branches, which are a smaller version of the branches growing on the limbs, which are a smaller version of the limbs growing on the trees. Another example is a universe, which is composed of a collection of spinning galaxies, which are composed of a collection of spinning solar systems which is a collection of spinning plants and so on. Each step is self-similar to the universe. Finally, a cloud exhibits self-similarity. A cumulus cloud is a collection of smaller puffs, which, in turn, are a compilation of smaller puffs and so on. Each puff is a smaller replica of the large puff. Fractals are often formed by an iterative process. That means that an operation is preformed on one figure to create a new figure. Then this operation is performed on the new figure to make another figure and so on. Each step of this process is called an iteration. An illustration of this is the diagram of Kochs snowflake on page two. It begins with a triangle Then an operation is performed on it and it becomes the Star of David. As the operation is repeated infinitely on the figure, it becomes an increasingly complex snowflake. Once a fractal, such as Sierpinskis Triangle, is created it is crucial to find out its dimension. The dimension of this fractal is greater than a line and less than a plane, so it is between 1 and 2. To find the exact dimension, one needs to follow a simple formula: The dimension (d) of a shape is the log of the number of copies (n) that are produced when the figures sides are doubled, divided by the log of 2 (logn / log2 =d or n=2d). The dimension of Sierpinskis Triangle would be the Log of 3, because you get three copies of the triangle when you double its sides, divided by the Log of 2. The final dimension is 1.58496250072115618145373894394782. .udf46d80821b12f4e5b58eef4f9557524 , .udf46d80821b12f4e5b58eef4f9557524 .postImageUrl , .udf46d80821b12f4e5b58eef4f9557524 .centered-text-area { min-height: 80px; position: relative; } .udf46d80821b12f4e5b58eef4f9557524 , .udf46d80821b12f4e5b58eef4f9557524:hover , .udf46d80821b12f4e5b58eef4f9557524:visited , .udf46d80821b12f4e5b58eef4f9557524:active { border:0!important; } .udf46d80821b12f4e5b58eef4f9557524 .clearfix:after { content: ""; display: table; clear: both; } .udf46d80821b12f4e5b58eef4f9557524 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .udf46d80821b12f4e5b58eef4f9557524:active , .udf46d80821b12f4e5b58eef4f9557524:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .udf46d80821b12f4e5b58eef4f9557524 .centered-text-area { width: 100%; position: relative ; } .udf46d80821b12f4e5b58eef4f9557524 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .udf46d80821b12f4e5b58eef4f9557524 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .udf46d80821b12f4e5b58eef4f9557524 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .udf46d80821b12f4e5b58eef4f9557524:hover .ctaButton { background-color: #34495E!important; } .udf46d80821b12f4e5b58eef4f9557524 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .udf46d80821b12f4e5b58eef4f9557524 .udf46d80821b12f4e5b58eef4f9557524-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .udf46d80821b12f4e5b58eef4f9557524:after { content: ""; display: block; clear: both; } READ: Mummification EssayThe human body is composed of many fractals. From the moment of fertilization, the cells of the egg and the sperm break up into two more cells, which, in turn, break up into two additional cells and so on. Each cell is self-similar to the entire collection of cells. This compilation exhibits the chaos theory. If one link in this collection is incorrect or missing, the entire organism can be ruined. It will collapse on itself creating a sickle cell. Some Africans have a disease called sickle cell anemia in which their blood cells have one bad amino acid chain in a protein of many hundred amino acids. These sickle cells clot and create a lot of pain for th e person afflicted with this disease. A body as a whole is a fractal. It is a group of dissimilar systems working together, which are composed of groups of dissimilar organs working together, which, in turn, are composed of groups of dissimilar tissues working together, which is a group of dissimilar cells working together, which is a group of dissimilar organelles working together. The body begins with the creation of cell organelles that are formed together to make a cell. These cells, as stated above, duplicate to form tissues, which duplicate to form organs and so on until a human body is conceived. Fractal research can be used to predict how complicated organ systems in the body will respond to changes. This is important for understanding how to treat diseases. BibliographyChaos, Encarta Encyclopedia, 2000. Choas Theory, Encarta Encyclopedia, 2000. Fractals, Encarta Encyclopedia, 2000. Fractals: An introduction Available. (online) http://www.planetclick.com/ratebar.mpl?siteID=1000000000024998. Lampton, Christopher, Science of Chaos (New York: Franklin Watts, 1992) 9-16. Lanius, Cynthia, Fractals Available. (online) http://math.rice.edu/lanius/frac. Laplante, Phil, Fractal Mania (New York: Windcrest/McGraw-Hill, 1994) 1-22.

What Are 2 Cents When Doing An Essay Writing? - How You Can Come Up With a Better Answer

What Are 2 Cents When Doing An Essay Writing? - How You Can Come Up With a Better AnswerThe question, what are 2 cents when doing an essay writing, is often asked by students who want to know where they can go for help when it comes to essay writing. Essay writing is not easy to master and it is also not easy to write a good essay. Moreover, it can be hard to come up with good topics to write about when doing an essay. However, it is not too difficult if you know the correct way of doing it.I learned this from one of my professors who said that you should never make the small things big. Instead, concentrate on the big things instead. He made this statement when he noticed that a student in his class was having a hard time coming up with a topic to write about. His teacher asked him what were 2 cents when doing an essay writing. The student didn't know what the question was about.The lesson here is that the teacher shouldn't always expect the student to find the answer. He just asked the student how many dollars he or she would have if he or she were to do this as an assignment and the student said two cents.What were two cents amount? The teacher was surprised when he heard this and he immediately realized that he and the student had just talked. Of course, he also realized that the student was serious.For your own benefit, he advised that instead of trying to find the answer, focus on the topic and the idea and you will surely come up with a dollar amount. Just think about it: do you know how much time and effort you will be saving if you focus on this instead of asking what are 2 cents when doing an essay writing?You see, your interest is what will make you come up with the two cents amount. So, instead of asking what are two cents when doing an essay writing, focus on the topic. Besides, if you focus on the topic, it will also help you come up with the two cents amount.The second thing to remember is that you don't want to become impatient. That's because p atience is not an emotion, but an act. If you feel impatient, the results will not be good at all.Remember to focus on the idea and to concentrate on the idea alone. In fact, if you are actually doing an essay writing, then you will only be focused on your topic and not on how much you will be spending.

How to Ask for Funding in a College Scholarship Essay

How to Ask for Funding in a College Scholarship EssayThere are several factors that you must consider when writing an AFRO Schloship Essay. Since this is your final paper for your Sophomore year, it is imperative that you have all of the facts correctly listed on your academic document. In order to successfully finish your essay, there are a few points that you must cover.The first step in how to ask for funding in a college scholarship essay is to list all of the facts that are listed on your academic record. You will need to describe all of the facts that you are researching and writing about. The reason that this is important is because the facts that you list on your application can go into as much detail as you choose. Without them, there is no way that you can properly meet the standards for your application.The second step to writing an AFRO Schloship Essay is to list your major in the academic document. This is probably the most important part of the entire document. List the major that you are interested in on your document as simply as possible. It is imperative that you add this information at the beginning of your document. Once you list the area that you are interested in, you can then list the major that you want to pursue.You will also need to include the number of your current school, your class, and your financial aid office. These three pieces of information will make your application easier to get approved with the school and the financial aid office. They will have your information, which makes the process much easier for them.Once you have listed the information that you are researching for your entire application, it is time to start filling in the details of what you are researching. This is where you will begin to list what your major is, your class, and your financial aid office. These will all be listed along side of your major, your class, and your financial aid office. This information is important and should be included.The third st ep to how to ask for funding in a college scholarship essay is to list the facts that you are researching. You will be able to write more quickly if you list the information that you need to research immediately. List what all the information is, including the area that you want to pursue and the name of the school.When you have all of the important facts that you need for your college scholarship essay, you will be able to write your essay much faster. This means that you will be able to get a much better grade when you are ready to submit your application. Remember that you will have to write an academic document for your final year in high school.If you want to succeed with your application, the most important aspect that you will need to remember is that you will need to provide accurate information. It is very important that you learn to write a good academic document for your application. This will help you get a much better grade and increase your chances of getting the colle ge scholarship that you are seeking.

How to Write a Good General English Essay Topic

How to Write a Good General English Essay TopicSo, you want to write a good general English essay topic. If you are really going to ace your examination, you need to know the right things to write and the right things to omit. Here are a few tips to help you.First of all, avoid general essays that discuss things such as sports or the weather. In general, these topics are not very interesting to read and generally don't get the student's point across well. If you are writing on a topic that is going to be an interesting read, then just go ahead and do it.General essay topics such as religion, politics, religion and politics are also bad topics to write about. It is no use having an essay about something so trivial and common as religion. Politics, though, is another story altogether. You could have an excellent argument in support of a political standpoint.The whole point of having a college education is to learn to think for yourself. When you have a chance to write about something t hat will be interesting to read and of course provide your students with interesting facts, you should take advantage of it.If, on the other hand, your professor makes a comment about an important issue, it would be advisable to note it down and to make a reference. This way, you can use it later when you are grading your papers and if you feel like defending your views, you can cite this essay.If you are unsure about how to write an essay, it is advised that you seek advice from the person who has a background in writing such an essay. You can speak to a writing tutor or even just to someone who writes regularly. Whatever you do, make sure that you read lots of essays before you start writing yours.There are many different sorts of essay topics that you can choose from. The problem is that most students have very little idea about what they should be writing about. Make sure that you do research and that you outline your topic in order to avoid getting too tangled up in the detail. Remember that general English essay topics are important. They are what the student will be writing about and should contain some relevant information that will give them some insight into the world around them.

Write A Wind Power Research Paper

Write A Wind Power Research PaperWind power research paper is a very exciting topic for anyone who is interested in a green future. We live in an era where we all must be committed to the fight against global warming. As a result, there are a lot of people who want to use alternative energy sources for their own personal needs. If you have ever considered purchasing an energy generator, there is a good chance that you have considered purchasing one in order to save the environment and to use renewable energy sources.One of the advantages of using a power generator is that it is able to produce your own power at home. You will no longer have to be dependent on someone else for your power needs. This could be especially useful if you are living in a place where there is not any other source of power to generate for your use.In order to write a wind power research paper, you will first need to gather as much information about the subject as possible. You can do this by doing an internet search or by talking to people that have already been involved in the field.Doing research is also important for generating additional research papers that you may be required to write on other topics that you find interesting. Although research is important, you still need to make sure that you are able to come up with an interesting thesis. The type of paper that you write will be based on what you have found from your research.It is important to keep in mind that there is a possibility that your research paper could be rejected due to plagiarism. This is something that you will need to take into consideration before you start writing your paper. If you have already come across some papers that have been plagiarized, you can still make use of research papers.Writing a research paper is also another way in which you can build your resume. If you know something about what is happening in the field of renewable energy, you can use it to create a unique product that can be used by ma ny other people. You can also show how well you know something about the subject matter if you have done your research properly.Writing a research paper is a great way to improve your abilities and knowledge in the field of renewable energy. Your dissertation can help you land a job as well as a degree. It is also a great way to help your future employer to improve their company by showing them that you know what you are talking about.