[HN Gopher] Show HN: Fractal Garden - An Exhibition of Mathemati...
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Show HN: Fractal Garden - An Exhibition of Mathematical Beauty
Author : trebeljahr
Score : 44 points
Date : 2022-10-09 19:48 UTC (3 hours ago)
(HTM) web link (www.fractal.garden)
(TXT) w3m dump (www.fractal.garden)
| umutcankus wrote:
| Really beautiful, thanks for your effort! I am trying to prepare
| a small presentation inspired by the book `The Computational
| Beauty of the Nature`for an introductory engineering course and
| some examples in this website can provide good visual material.
|
| edit: also would appricate to able to zoom in.
| trebeljahr wrote:
| The Computational Beauty of Nature is such a cool book!
|
| There is also ABOP - the Algorithmic Beauty of Plants
| http://algorithmicbotany.org/papers/#abop which has been a huge
| inspiration for this project.
| trebeljahr wrote:
| Hi HN,
|
| in September I built this website, which explores some
| mesmerizing fractals. The idea behind it is to have a beautiful
| "garden" that instead of being filled with flowers and plants is
| filled with magnificent mathematical objects. The fractals are
| all interactive and you can play around with the options,
| changing colors, iterations, and more.
|
| The whole thing is open source, so if you feel like it and have
| the time, please contribute to the project. It's tagged for the
| Hacktoberfest and contributions count toward your Hacktoberfest
| progress! Here's the link to the GitHub:
| https://github.com/trebeljahr/fractal-garden
|
| The fractal garden, as such is part of what I am trying to do
| right now, picking awesome projects I always wanted to do and
| that are just outside my comfort zone (in terms of skills or
| knowledge). I then try to build as much of them as I can within a
| month, before moving on to the next project the next month.
|
| I write summaries of the learnings I had during the projects on
| https://www.trebeljahr.com/
|
| Let me know what you think and the ideas and feedback you have.
|
| Enjoy your day and take care.
|
| Cheers, Rico
| aintmeit wrote:
| Hey you! I've read the blog. It's magnificent. I looked at your
| garden. It's incredible. Love love love. Live, laugh, love.
| Cheers.
| Zhyl wrote:
| It doesn't seem like you can zoom very far (on Android, at
| least), which to me undermines quite a lot of the wonder of
| fractals.
| [deleted]
| trebeljahr wrote:
| This is sadly true and I whole-heartedly agree with you...
|
| It's because I didn't find a way to construct only parts of
| the fractals based on the viewport. Many of the fractals you
| can see in the garden are generated iteration by iteration
| and generating the next iteration for only the visible part
| is not a trivial problem to solve... I struggled thinking
| about a solution for this, but in the end gave up in favor of
| having more fractals.
|
| For the Mandelbrot Set the above is not the case, but the
| zoom there is still very limited due to precision issues in
| WebGl (a float has only limited bits, even for high precision
| floats) and things get horribly slow if trying to implement
| arbitrary precision on the GPU.
|
| There are some ideas around "perturbation theory" that can
| help to get more zoom on the Mandelbrot Set (still not
| infinite) but I had a very hard time wrapping my head around
| how to implement that in a shader.
|
| But please, if you have ideas of how to fix this - the
| project is open source and it would be 100% awesome if it
| were possible to nicely zoom in/out of all of them.
|
| I opened an issue on the repo:
| https://github.com/trebeljahr/fractal-garden/issues/22
| anigbrowl wrote:
| It's very nice and I look forward to adding to to it.
|
| I wonder if you(or someone else) knows of a general tool for
| exploring L-systems? As you comment, 'all L-systems are
| related', but I've had a hard time navigating the theoretical
| literature on this. For several years now I've been looking for
| a way to examine a tree or other network and extrapolate a
| structural 'recipe' for it. I'll get this _Algorithmic Beauty
| of Plants_ book but would love to hear of any resources you
| know for 'reverse engineering' L-systems from existing tree
| structures.
| trebeljahr wrote:
| I have no idea honestly...
|
| One pointer that might be worth exploring, which is not quite
| L-Systems but might be related is Fractal Compression. I've
| read that there are algorithms to compress images into a
| "closest" IFS - iterated function system.
|
| https://en.wikipedia.org/wiki/Fractal_compression
|
| Maybe one could come up with a way of going from an image via
| fractal compression to an IFS which could then be used as the
| basis for an L-system?
|
| Most of the L-Systems that are on this site are from Paul
| Bourke - http://paulbourke.net/fractals/lsys/
|
| Which is a really awesome resource!
| anigbrowl wrote:
| Thanks, these are really great resources and I'm looking
| forward to exploring them. It's striking to me that so much
| work was done on this in the 1990s and early 2000s and that
| the subfield seems to have (mostly) been overlooked since.
| trebeljahr wrote:
| also Wikipedia says that this is an open problem. However,
| with the "citation needed" warning...
|
| https://en.wikipedia.org/wiki/L-system#Open_problems:~:text=.
| ...
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(page generated 2022-10-09 23:00 UTC)