Fractals: The Organization of Chaos :: Mathematics Geometry Essays

Fractals: The Organization of Chaos Please ignore the references to pictures or figures. I no longer have them, so I could not include them on this page. Thanks. Fractals are a relatively new concept in geometry. Most concepts for Euclidean geomtery, the division of geometry which deals with lines, circles, triangles, and other standard shapes, stem from the Late Greek and Early Rioman times. Considering the age of mathematics, the study of fractals is new becasue it dates to the beginning of this century. However, the age of computers brought about an explosion into this yet untamed universe of math. As Heinz-Otto Peitgen and Dietmar Saupe remark in the preface for The Science of Fractal Images, "Computer graphics has played an essential role both in its development and rapidly growing popularity" (V). Before this, mathematicians could only visualize what they were discussing (Mandelbrot, Fractals: Form, Chance, and Dimension 2). But now, fractals are the mathematician's answer to chaos and therefore can be used to help scientists better understand nuature and the universe. Scientists can define any structure from a snowflake to a mountain o r even an entire planet with this new division in Mathematics. Thus, fractals define our universe. Benoit B. Mandelbrot is a key figure behind the rise of this new science. A Professor of mathematical Sciences at Yale and an IBM Fellow, Mandelbrot is the man who coined the term "fractal" in 1975. Mathematicians, such as Gaston Julia, only defined them as sets before this and could only give properties of these sets. Also, there was no way for these early fractal researchers to see what they were hypothesizing about. As Mandelbrot states in The Fractal Geometry of Nature, "I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means 'to break...'" (4). Mandelbrot used this particular root because of how he defines fractals. Unlike Euclidean geometry, which has its figures in a particular dimension (e.g. a square is two-dimensional), fractals have fractional dimensions. They do not exist in just one dimension but can encompass part of another. For example, as Mort La Brecque states in his article on fractals in the Academic American Encyclopedia "a natural fractal of fractal dimension 2.8 ... would be a spongelike shape that is nearly three dimensional in its appearance. A natural fractal of fractal dimension 2.2 would be a much smoother object that just misses being flat" (105-106, Mandelbrot "Fractals").

Of Mice and Men Essay

John Steinbeck provides a variety of different attitudes towards women in the novel ‘Of Mice and Men. ’ I will explore these attitudes in order to represent the portrayal of women in the book; in which there are many different women with different attitudes respectively. Steinbeck uses the portrayal of Curley’s wife, who is the main female protagonist to show how women were treated during the 1930’s ‘Depression era. ’ The women I will analyse are Curley’s wife, Aunt Clara, Susy, Clara, The woman in Weed and Curley’s wife’s mother. In the novel, women play a significant role as they are featured in every scene of the story. However their roles can be defined negatively for they are portrayed as weak and as possessions of men. Steinbeck displays many different women who are displayed from a man’s perspective in a sexist era. The reader’s first encounter with a female character is ‘The woman in Weed. ’ She is presented as a liar and exaggerator due to her reaction when Lennie tugged her dress. George and Lennie are forced to flee from Weed, in order to escape the newly formed mob chasing them. This forces the reader to perceive women in a diminishing way at the start, which influences the reader’s perception on women overall, throughout the novel. After the initial encounter with a woman the reader is encouraged to believe that ‘The woman in Weed’ seemed to be the root cause of George and Lennie’s dilemma. This idea of women being pest-like, poison and objects of sexual desire is played on throughout the novel. This ideology is presented in the likes of Susy and Clara. Susy and Clara were both brothel owners, this job taken by both women suggests the type of jobs available for women at the time. Steinbeck presents life when the ranch workers go to the whore house. This suggests that women were seen as just a pass time during the 1930s and no-one had any respect for them. This shows how women were seen as being an object used to have fun not to socialise with. The job they possess, in comparison with Curley’s wife’s role, shows how Steinbeck displays the role of women in the novel. The language and context causes the reader to perceive women as objects that have to cater for a man’s every whim. Steinbeck provides the reader with one relatively positive role of a woman throughout the novel, in the form of Lennie’s ‘Aunt Clara. Aunt Clara is not his mother, but she has taken on the maternal role and it is implied that she is a blood relative. She is a flat character but when she is talked about, it is in a respectful tone. We can guess that from the way Lennie talks to her in his mind in the last pages that she has high standards; Lennie says à ¢â‚¬Ëœma’am’. This shows that Lennie respects her. The use of ‘Aunt Clara’ provides the reader with mixed attitudes towards women in the story. Yet this positive image of women is overlooked as the reader meets the likes of Curley’s wife and her mother. Curley’s wife’s mother is represented as conniving and jealous, due to her involvement in Curley’s wife’s life. Curley’s wife is changed from becoming a movie star and following the ‘American dream,’ to living with Curley, a dominant and sexist man who doesn’t allow her to be free. Throughout the novel the reader is expectant to distinguish women as possessions, this expectation is significantly shown with Curley’s wife. Curley’s wife is the main woman presented in the book. Her tone of language and the type of language connected to her is the same as the stereotypical depiction of women in the 1930’s. She is subjected to sexist beliefs which essentially pave the way to her death, for if she hadn’t sought attention from Lennie who seemed to be one of the only men to speak to her, she wouldn’t be dead. Steinbeck presents the women in the novel as being an object, not like normal people just because they are women and they believe men are superior. Men believe they own women and can treat them how they want to. In the novel, the women are socially inferior to the men and men just see them as possessions or objects. Curley’s wife is nameless which suggests that she is insignificant and unimportant, and that she is not treated like the men on the ranch who all have names. The importance of her character is crucial for the story’s development. The apostrophe in ‘Curley’s’ suggests that she belongs to Curley as if she is just an object. Also, when we find out that Curley’s glove is full of Vaseline, it implies that he likes petting his wife, just like Lennie like petting dogs, mice and rabbits. This suggests that Curley thinks of his wife like an animal. It also gives the implication that he needs to please her but there is no love in their relationship. Curley is proud of his wife, especially when she makes others envious of him. However, he has no respect for his wife and shows her off like a trophy wife. Later on in the novel, we find out that Curley’s wife doesn’t actually love Curley, and only married him in the hope of escaping a lonely, dull life. ‘I don’t like Curley. He ain’t a nice fella. ’ She seems preoccupied with strategies to avoid detection from her husband and manages this by continuously asking of his whereabouts. ‘Have any of you boys seen Curley? ’ Like George, Lenny and later on Candy, Curley’s wife has a dream despite it being one of great contrast to theirs. The futility of dreams is ever present within the novel. Curley’s wife has an ambition to work in films ‘coulda been in the movies and worn nice clothes’ and this is no doubt stemmed from her desire for attention and is linked to her loneliness and insecurities on the ranch as she bitterly resents not being treated as an individual. Men make promises to her ‘he says he was gonna out me in the movies’ but she appears to lack the intelligence to realise the emptiness of their promises. This means that women were presented to have a lack of intelligence and were only there to look good. Steinbeck presents women as objects of forbidden lust. The word â€Å"jail bait† is used to describe Curley’s wife repeatedly throughout the novel, this word describes his wife in a way that presents her as a very attractive young girl, but the term jail bait can also be used to show that she is a danger to toy with. Despite the fact that she is constantly flaunting herself, if she is approached in any way it will cause conflict with Curley which could result in an altercation that could cause a prison sentence. Hence her being bait, to end up in jail. ‘†¦ Yeah? married two weeks and got the eye’ Using these words Steinbeck is implying that all women start looking at other men only two weeks after being wed. The words ‘the eye’ suggests it’s like a disease you can get which will make you look at other men instead of your own. The reader is able to recognise the negative atmosphere when Curley’s wife is mentioned, through the language and attitudes of the ranch workers associated with Curley’s wife. â€Å"Curley’s married †¦ a tart. † This shows how George values women very little as he calls Curley’s wife â€Å"a tart†. This could be judged as prejudice as he does not fully know her and jumps to conclusion. However in the book john Steinbeck presents women in a negative fashion, for example Curley’s wife is very provocative and dwells on men’s feelings and takes advantage of them. John Steinbeck’s view represents that of many people during the 1930’s. John Steinbeck’s use of colour symbolism can be interpreted through Curley’s wife. Curley’s wife is connected with the colour red. The colour red is also linked with ‘The woman in Weed,’ this suggests that George’s negative attitude towards women like Curley’s wife, is associated with his stereotype of women, due to his previously bad encounters with them. The colour red can be associated with danger, romance, lust and blood. This suggests that the use of the colour red with women provides the reader with belief that they may be associated with danger, romance, lust and blood. The story surrounded by the actions of Curley’s wife can be interpreted through the likes of Genesis and Greek Mythology. In Genesis, Adam and Eve are met with a serpent who beguiles them to eat fruit from the tree which god had instructed them not to eat from. In consequence they are expelled from heaven. This can be interpreted as Curley’s wife being the serpent and George and Lennie being Adam and Eve, as Curley’s wife creates the obstruction of fulfilling the dream George and Lennie had of owning their own house. In Greek Mythology, Sirens lure sailors to their death. Sirens are seductive female creatures in Greek Mythology. The role of Sirens can be interpreted through Curley’s wife. The Sirens seduce sailors to their deaths. Due to the use of language used by Steinbeck, the reader is forced to accept the role of Curley’s wife as a version of a Siren. Curley’s wife is, socially speaking, a marginal figure. She is a minority and has very little power in the world. She is introduced as a â€Å"tart† and a trouble-maker, Curley’s wife is presented in increasingly sympathetic ways as the novel progresses. In the end, instead of being a trouble-maker, Curley’s wife is a victim. Not only is she is victim of a murder, but she is also a victim of circumstance, having married to get away from home only to find herself trapped on the ranch where she has no friends, nothing to do, and is allowed only one relationship. The reader is forced to see her death as sympathising, as the death of someone young is more painful than of an elder. To conclude I will provide my own opinion regarding the different attitudes towards women in the novel ‘Of Mice and Men. ’ As a reader, my intake on this situation is that Steinbeck uses a variety of techniques that portray women in different senses. However, these different attitudes are put aside as they are overpowered by the ideology that women are inferior to men and that they are their possessions.

The Importance Of Contact Information For The Director And...

Keep in contact with appropriate Content Specialist(s). †¢ Participate in triplet meetings and officer transitions to help ensure a smooth transition and transfer of materials and information. Keep a well-organized, complete notebook to provide continuity from one adviser to the next. Train successor. Adviser Notebooks Each adviser, regardless of her committee assignment, should keep the following items in a notebook or in a file electronically that she brings with her to Advisory Board meetings and meetings with her committee or officer. The contact information for the officers and members can be found in KeyReports. 1. Lists a. Advisory Board roster b. Roster of local association officers (if applicable) c. Contact information for the†¦show more content†¦Copies of correspondence and memoranda received from the campus and the community related to committee work c. Communication from local alumnae association(s) (one year) 6. Resources a. Kappa Kappa Gamma Fraternity Bylaws, Standing Rules and Policies b. Chapter Bylaws and Standing Rules c. Leadership Guides d. What To Do When for Chapters e. Robert’s Rules of Order, Newly Revised Chapter Council Adviser The Chapter Council Adviser should have knowledge and experience related to the Fraternity’s organization and a basic understanding of parliamentary procedure as she works with the executive body of the chapter. †¢ Attend Chapter Council meetings or ensure another adviser attends any meeting she cannot attend. †¢ Advise and assist Chapter Council in all of its work. †¢ Grant excuses for absences from Initiation. †¢ Advise the chapter President. †¢ Advise the chapter Nominating Committee unless Advisory Board appoints another adviser. †¢ Be present for chapter officer elections or ensure that another adviser will attend. †¢ Be present when chapter Bylaws and/or Standing Rules are revised and voted upon. †¢ Serve as member ex officio of House Board and attend House Board meetings with the chapter President. †¢ Serve as a member of the chapter’s Emergency Procedure Team. †¢ Assist in trainingShow MoreRelatedInternet Mark eting For Growing Civil Engineering Firm1286 Words   |  6 Pagesbe online. †¢ Main conclusions: o Imperative to have an updated and interactive online strategy. o To look for creative but honest ways to connect with target audience that is technologically advancing. †¢ I recommend the development of an internet content and marketing plan that includes clear strategies and goals to build up a positive and transparent brand. INTRODUCTION †¢ Purpose: Noticed potential business and networking opportunities were being overlooked because the company lacks an online andRead MoreRisk Communication At The National Research Council ( Nrc )2326 Words   |  10 PagesThe National Research Council (NRC) (NRC, 1989) defines risk communication as an interactive process of exchange of information and opinion among individuals, groups, and institutions. The primary role of risk communication is to provide information to the public to induce appropriate levels of concern and actions (Covello, McCallum, Pavlova, 1987). 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Alternatives Recommendation†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. 7 IV. Implementation†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦ 9 References†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦... 16 1 Executive Summary Molson Canada has been facing negative reactions their recent social media marketing initiativeRead MorePhase 14843 Words   |  20 Pagesï » ¿Busi 454 Simulation : Phase 1 Duplox Copiers Canada Limited Carlos del Aguila Contents Section A 2 Section B 4 Section C 8 Section D 14 Section E 22 Section A Duplox Copiers Canada Limited is experiencing several severe issues that are affecting the profitability of the firm. 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