4 ms·

Brainfilling Curves - a Fractal Bestiary (online book)

17 points by ohwp 13y ago

Smerity 13y ago
This is a beautiful book -- thanks for pointing it out! It's a graphical and mathematically light introduction to many of the areas in which fractals / space-filling curves intersect with programming, even if it's not explicitly pointed out. For example, on their page covering Node-Replacement Curves[1], they mention both Hilbert Curves and Z-Order Curves. They don't describe them heavily there, but they're used in many spatial databases to allow for efficient indexing of two or more dimensional data. Google Maps[2] for example uses Hilbert Curves internally to allow for fast querying of queries such as "shops within 5km of your house". They've also open sourced numerous libraries that perform these calculations[3][4]. The book interface itself is also quite nice, though I still prefer the PDF copy you can get by hitting the Information button (i) on the top right. Edit: Wow. I thought that PDF was taking a while to load: the PDF is over 200MB. Maybe best to explore the book online! [1]: http://archive.org/stream/BrainfillingCurves-AFractalBestiary/BrainFilling#page/n27/mode/2up http://archive.org/stream/BrainfillingCurves-AFractalBestiar... [2]: http://www.vldb.org/pvldb/vol4/p290-venetis.pdf http://www.vldb.org/pvldb/vol4/p290-venetis.pdf [3]: https://code.google.com/p/s2-geometry-library/ https://code.google.com/p/s2-geometry-library/ [4]: http://google-opensource.blogspot.com.au/2008/08/uzaygezen-multi-dimensional-indexing.html http://google-opensource.blogspot.com.au/2008/08/uzaygezen-m...
- ohwp 13y ago
  I like the simple explanations in the book. Also check the authors website for more fractal and graphic goodness: http://www.ventrella.com/ http://www.ventrella.com/ Edit: more about the author: http://en.wikipedia.org/wiki/Jeffrey_Ventrella http://en.wikipedia.org/wiki/Jeffrey_Ventrella
- keenerd 13y ago
  > Wow. I thought that PDF was taking a while to load: the PDF is over 200MB. The Djvu file is 13MB. (To read these, I use DjView.) http://ia701203.us.archive.org/22/items/BrainfillingCurves-AFractalBestiary/BrainFilling.djvu http://ia701203.us.archive.org/22/items/BrainfillingCurves-A...
  - tiziano88 13y ago
    I prefer the epub version now that Google play books supports side loading of such files (kindle has been doing the same for a while already I think)

17 points by ohwp 13y ago

This is a beautiful book -- thanks for pointing it out! It's a graphical and mathematically light introduction to many of the areas in which fractals / space-filling curves intersect with programming, even if it's not explicitly pointed out. For example, on their page covering Node-Replacement Curves[1], they mention both Hilbert Curves and Z-Order Curves. They don't describe them heavily there, but they're used in many spatial databases to allow for efficient indexing of two or more dimensional data. Google Maps[2] for example uses Hilbert Curves internally to allow for fast querying of queries such as "shops within 5km of your house". They've also open sourced numerous libraries that perform these calculations[3][4]. The book interface itself is also quite nice, though I still prefer the PDF copy you can get by hitting the Information button (i) on the top right. Edit: Wow. I thought that PDF was taking a while to load: the PDF is over 200MB. Maybe best to explore the book online! [1]: http://archive.org/stream/BrainfillingCurves-AFractalBestiary/BrainFilling#page/n27/mode/2up http://archive.org/stream/BrainfillingCurves-AFractalBestiar... [2]: http://www.vldb.org/pvldb/vol4/p290-venetis.pdf http://www.vldb.org/pvldb/vol4/p290-venetis.pdf [3]: https://code.google.com/p/s2-geometry-library/ https://code.google.com/p/s2-geometry-library/ [4]: http://google-opensource.blogspot.com.au/2008/08/uzaygezen-multi-dimensional-indexing.html http://google-opensource.blogspot.com.au/2008/08/uzaygezen-m...

ohwp 13y ago
I like the simple explanations in the book. Also check the authors website for more fractal and graphic goodness: http://www.ventrella.com/ http://www.ventrella.com/ Edit: more about the author: http://en.wikipedia.org/wiki/Jeffrey_Ventrella http://en.wikipedia.org/wiki/Jeffrey_Ventrella
keenerd 13y ago
> Wow. I thought that PDF was taking a while to load: the PDF is over 200MB. The Djvu file is 13MB. (To read these, I use DjView.) http://ia701203.us.archive.org/22/items/BrainfillingCurves-AFractalBestiary/BrainFilling.djvu http://ia701203.us.archive.org/22/items/BrainfillingCurves-A...
- tiziano88 13y ago
  I prefer the epub version now that Google play books supports side loading of such files (kindle has been doing the same for a while already I think)