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mario837 — Understanding Fractals
Published: 2010-10-10 13:41:33 +0000 UTC; Views: 6366; Favourites: 75; Downloads: 643
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Description
Wikipedia has a good amount of information available on fractals plus the possibility of collecting them in a so called "book".As I am not a full contributor of Wiki, I was not allowed to save the result in their server, so I am uploading it here as a PDF.
I have tried to avoid the purely mathematical stuff, only reserved for my friend (and his friends)
The very nature of Wiki will provide you with a myriad of links to dig deep into the preferred subjects.
I hope that at least some of you that can find some subjects of interest. In my case, I was quite surprised for what I compiled under the Chapter "Fractal Applications".
A final warning: if you decide to download the paper, it weighs 72Mb.
Below is a list of the articles with the chapter organization I have given them, so you have an rough idea of what is all about.
Contents
Articles
Some Basics 1
Benoît Mandelbrot 1
Fractal 7
Fractal dimension 14
Dimension 17
Attractor 24
Complex number 29
Self-similarity 43
Fractal flame 45
Orbit trap 47
Chaos theory 49
Brownian motion 62
Perlin noise 69
Famous Fractals 71
Mandelbrot set 71
Julia set 89
Sierpinski triangle 98
Newton fractal 103
Pythagoras tree 106
Lyapunov fractal 107
Lorenz attractor 109
L-system 113
Iterated function system 127
Barnsley fern 131
3D Fractals 135
Mandelbox 135
Mandelbulb 136
Fractal Applications 138
Fractal antenna 138
Fractal landscape 141
Algorithmic composition 143
Lichtenberg figure 148
Fractal compression 151
Fractal in soil mechanics 155
Elliott wave principle 156
Wolfram Demonstrations Project 162
Invariant set postulate 164
The Sacred Side of Fractals 166
Sacred geometry 166
Fractal cosmology 171
Fibonacci number 175
Golden spiral 190
Golden ratio 193
Mandala 214
Sri Yantra 222
Tree of life 224
Fractal Software 235
Fractal-generating software 235
Fractint 237
Apophysis (software) 239
Ultra Fractal 241
Sterling (program) 243
XaoS 245
Fractal Art 247
Digital art 247
Systems art 254
Fractal art 258
The Beauty of Fractals 261
Other Fractal Formulas 264
Apollonian gasket 264
Cantor set 271
Cantor function 277
H tree 279
Hexaflake 281
Douady rabbit 282
Hausdorff dimension 285
Lute of Pythagoras 290
Multibrot set 291
Multiplicative cascade 295
Nova fractal 297
Pickover stalk 300
Sierpiński arrowhead curve 301
Sierpinski carpet 302
Siegel disc 304
Vicsek fractal 307
Dragon curve 309
Koch snowflake 315
Lévy C curve 320
Space-filling curve 322
Appendix 327
List of fractals by Hausdorff dimension 327
Romanesco broccoli 340
Proportion (architecture) 342
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension 351
References
Article Sources and Contributors 353
Image Sources, Licenses and Contributors 360
Article Licenses
License 370
Related content
Comments: 68
Mario, thank you so very much for having compiled these and sharing them with us!
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Thank you, looks very interesting indeed. I have downloaded and will read...
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This is very interesting! thanks for sharing!
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nice one Mario ,, look forward to reading it.. maybe it will help me understand a little
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Thank you Tim! I am sure you will find section interesting.
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I thought you said there was not so much math in it!!!! my head is spinning 
but seriously, it is very informative I only wish I had even a rudimentary understanding of the mathematics involved, it frustrates me that the equations leave me blind to a landscape I wish I could see !
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Unfortunately math is of the essence though I think it is not necessary to go into most of it.
I hope your eyes heal soon and your head stops spinning!
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Thanks a lot for these articles! I gave you a well deserved llama badge!
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You are welcome and thanks for the badge!
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Thank you for this mario. Could I get a copy of the mathematical wiki articles as well?
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I am sorry Francis but I didn't gather them. However, you can follow the links contained there.
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Thank you so much for doing this! It is a blessing!
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Thank you very much! I only hope it is useful.
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I'll download the zip when arrivesd to my own computer
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Thanks Ingvar and I hope you find something useful there.
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Wow this is amazing Mario and I just stumbled across it looking for which formula it is that makes the Barnsley tree type objects in Mbd3...do you have any suggestions on that? Thanks!
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The undisputed Master of Formulas is so I would ask him or read his comments to the Barnsley formulas he made for MB3D. BTW Barnsley is one of his worst nightmares.
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OH great! LOL! So far, I'm not seeing how to use them at all!
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Neither Luca!
This is the type of thing you can get [link]
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Wow that is interesting! If I wasn't already in the midst of soooo many series! lol! I sure wish I had a bigger faster computer - or better yet, and extra one dedicated to rendering alone!
I do see a lot of MB3D's with Barnsleyesque patterns doing what the Barnsleys in UF do. And there is some tree like action going on in them! Well, it's for a longer term theme like idea so no rush! LOL!
Thanks for all the tips!
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Great! I'm just starting in the fractal world, and I believe this is just what I needed...
First the basics... jeje Thank You very much!
Mmmm Disculpa una pregunta, será que existen estos artículos en español?
Jeje No te preocupes... viendo la Wiki... Gracias
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Gracias por el comentario. Espero que te resulte útil.
En cuanto a idioma, te aconsejo que insteles el Google Chrome que tiene un traductor de sitios bastante aceptable. En este caso, tal vez te convenga recorrer el tutorial de Titia van Beugen que está en Holandés pero se entiende bastante bien en la traducción Chrome al Español. Lo vas a encontrar acá [link]
Está referido a Fractal Explorer que me parece la mejor puerta de entrada al mundo de los fractales, antes de probar otros progrmas más complejos.
Cualquier duda a tu disposición.
Saludos,
Mario
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Muchas gracias por la información
Seguiré tu consejo y seguiré con el Fractal Explorer...
Gracias, Un Placer.
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I don't think I ever told you thanks for these.
II appreciate them, and you taking the time to get them together.
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I can't wait to begin to browse through this, Mario...
what a tribute to him, this work!!!
you, sir, are a scholar and a gentleman!!!
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Thank you Janet. I hope you find some interesting new material there
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you're most welcome, Mario!!!
I know I will!!!
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Thank you for this! It is very useful to us fractal artists.
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For hours and hours, without break!
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To consult if and when necessary.
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Thanks Lea
I hope it has come out interesting as it has to be made in one session.
As you see it was sort of premonitory, made just 4 days before hes passing
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