Free Essays on Fractals

In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular bumps, plus numerous thin filaments, which branch out in uneven shapes and contain small islands shaped like miniature versions of the main section. Their results were of mild interest to a small group of pure mathematicions, and were ignored by everyone else. In the 1970s, an applied mathematician, Benoit Mandelbrot, working at the IBM Research Laboratory, did some computer simulations for these sets on the reasonable assumption that, if you wanted to prove something, it might be helpful to know the answer ahead of time. Mandelbrot had been one of Julia's students in 1945, and he was familiar with the papers of both Julia and Fatou. IBM had the best computers available, and a policy of letting research staff members have lots of free computer time to work on anything in which they were interested. Of course, they were also expected to do something useful occasionally. In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular ... Free Essays on Fractals Free Essays on Fractals In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular bumps, plus numerous thin filaments, which branch out in uneven shapes and contain small islands shaped like miniature versions of the main section. Their results were of mild interest to a small group of pure mathematicions, and were ignored by everyone else. In the 1970s, an applied mathematician, Benoit Mandelbrot, working at the IBM Research Laboratory, did some computer simulations for these sets on the reasonable assumption that, if you wanted to prove something, it might be helpful to know the answer ahead of time. Mandelbrot had been one of Julia's students in 1945, and he was familiar with the papers of both Julia and Fatou. IBM had the best computers available, and a policy of letting research staff members have lots of free computer time to work on anything in which they were interested. Of course, they were also expected to do something useful occasionally. In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular ...

Free Essays on A Great Philosopher King

â€Å"A Great Philosopher King† The Philosopher King in someone who come closest to the form of goodness, goodness itself. The Philosopher King will know what is the best for his or her people because of the desire and love for knowledge. The Philosopher King can view things that ordinary people do not see. The person that I feel that could have come closest to Plato’s theory was a great woman who lived to help others. Mother Teresa who real name is Agnes Gonxha Bojaxhiu, was born in Skopje, Yugoslavia in year 1910. She took her vow in 1928 as a nun, and then she taught in St. Mary’s High School in Calcutta for nineteen years. The suffering and poverty outside of the convert made her devote herself to working among the poor in the slums of Calcutta. Without money she started an open-air school for homeless children. Voluntary helpers, and financial support was given from church organizations, which made it possible for her to extend her work. In Oct. 7, 1950 she received permission to start her own order called â€Å"The Missionaries of Charity,† the primary goal was to love and care for those people that one cares about. She established fifty relief projects operating in India. In these relief projects she helped slum-dwellers, children’s homes, homes for the dying, clinics and a leper colony. The projects have spread in Africa, Asia, Latin America, Italy, Great Britain, Ireland and United States. Mother Teresa has caught the attention of the world; she has received awards for her goodness. In 1971 she received the Pope John XXIII Peace Prize. In 1972 she received the Nehru Prize for her promotion of international peace and understanding. The last award she got was in 1979 the Balzan Prize for promoting peace and brotherhood among the nations. â€Å"I choose the poverty of our poor people. But I am graceful to receive (the Nobel) in the name of the hungry, the naked, the homeless, of the crippled, of the blind, of th... Free Essays on A Great Philosopher King Free Essays on A Great Philosopher King â€Å"A Great Philosopher King† The Philosopher King in someone who come closest to the form of goodness, goodness itself. The Philosopher King will know what is the best for his or her people because of the desire and love for knowledge. The Philosopher King can view things that ordinary people do not see. The person that I feel that could have come closest to Plato’s theory was a great woman who lived to help others. Mother Teresa who real name is Agnes Gonxha Bojaxhiu, was born in Skopje, Yugoslavia in year 1910. She took her vow in 1928 as a nun, and then she taught in St. Mary’s High School in Calcutta for nineteen years. The suffering and poverty outside of the convert made her devote herself to working among the poor in the slums of Calcutta. Without money she started an open-air school for homeless children. Voluntary helpers, and financial support was given from church organizations, which made it possible for her to extend her work. In Oct. 7, 1950 she received permission to start her own order called â€Å"The Missionaries of Charity,† the primary goal was to love and care for those people that one cares about. She established fifty relief projects operating in India. In these relief projects she helped slum-dwellers, children’s homes, homes for the dying, clinics and a leper colony. The projects have spread in Africa, Asia, Latin America, Italy, Great Britain, Ireland and United States. Mother Teresa has caught the attention of the world; she has received awards for her goodness. In 1971 she received the Pope John XXIII Peace Prize. In 1972 she received the Nehru Prize for her promotion of international peace and understanding. The last award she got was in 1979 the Balzan Prize for promoting peace and brotherhood among the nations. â€Å"I choose the poverty of our poor people. But I am graceful to receive (the Nobel) in the name of the hungry, the naked, the homeless, of the crippled, of the blind, of th...

Archaeology Essay Example | Topics and Well Written Essays - 2000 words

Archaeology - Essay Example The white conquers spreading of disease and war is thought to have driven the royal family and servants from Machu Picchu. This is a fascinating subject that can be researched with pleasure. Machu Picchu is an abandoned Inca site. Although it is thought that Hiram Bingham (2004) â€Å"discovered† the city, a few others had been there before (219). MacQuarrie (2008) reports Bingham found the engravings of â€Å"M. Eugene de Sartiges, 1834†, â€Å"Jose Maria Tejada, Marcelino Leon, 1834†, â€Å"Jose Benigo Samnez, Juan Manual Rivas Plata, Mariana Cisneros, 1861†, and â€Å"Pio Mogrovejo, July 4, 1885† (384). Bingham was the first to bring attention to the city. Machu Picchu is located between the ridges of Machu Picchu (hence the name) and Pisac in the South American country, Peru according to D’Altroy (2003:127). The find of an intact abandoned Inca site was a major discovery for archeology and architectural studies. Machu Picchu allowed for the study of the Inca way of life and architectural ways. Bingham according to Burger and Salazar (2008) removed artifacts from the site to examine at Yale University (2). Machu Picchu has been explored by many more scientists and tourists since Bingham’s discovery in 1911 of the site D’Altroy (2003) (21). The majestic Inca site has been an uncovered jewel ever since. The Incas were a South American people before the Spanish conquest. D’Altroy (2003) explains Incas did not have a written language, but did have an oral history that has passed traditions down through the generations (121). Without the oral traditions, little or no knowledge might have been known about the Incas. The Spanish records after the Spanish expedition into also provide an insight into the Inca way of life, but only from an invader’s perspective Burger and Salazar 2005:2). Incas did share their oral traditions with the Spanish, but