Take care that I'm not a mathematician and I don't know too much more than the calculus shown to engineers, but I still liked to believe I can find something interesting and new if I search time enought. Well, I must say that I'm happy anywat to have discovered many things before knowing about them thru technical books on the subject. That's the case for the first serius investigation I made in 2001-2002. It ended up with a PDF you will find below. Two years later I bought the book "Complex Dynamical Systems" by R.L.Devaney and I understood that I didn't discover anything not known to the experts on the subject that studied the field in the 80's. In fact I discovered that there was so much that I didn't know - however I was happy to see that, once more, my intuition had lead me to the right direction.
mandelbrot set
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My first paper "De la dinámica a la geometría en el conjunto de Mandelbrot" (From dynamics to geometry on the Mandelbrot set). Done during 2001 and 2002 and presented to the Arquimedes contest in Spain. I didn't pass even the first selection. It was a complete recopilation of my discoveries on the Mandelbrot set done since 1999. Some of them experimental, other theorethical, but quite interesting all of them anyway. Written from somebody with not too much mathematic knowledge, should be readable by any engineer or similar degree student. I hope it helps to create curiosity on the subject to some people, specially those that like to "see" the maths on screen. I'm sorry to say it is written in spanish, I will translate it to english as soon as possible, and probably I will update it with some new demonstrations. Anyway, for some of the discoveries I made, and to learn many other things, I recomend you to read Devaney's articles and books on the net. |
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Few experiments and results on the Mandelbrot for polynomials z^k+c, a winter weekend of March 2006. Still basic level, but interesting for those people starting to inspect the maths behind the images. May be few nice and usefull results. Written in English this time, I hope to review it when my grammar improves. |
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general
| This one is not really a resarch paper, but just something I made with Borja Sierra for "Aula Iberdrola" in 2003. It's a small educational application showing the basic principles of fractal geometry. Contains easy to undersand examples to play with in real time, and some html like navigation system. It is just 70% finished, and it's in spanish. It might help for those teachers of schools that want to explain what fractal geometry is to young students. |
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