[HN Gopher] Show HN: Fractal Garden - An Exhibition of Mathemati... ___________________________________________________________________ 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=. | ... ___________________________________________________________________ (page generated 2022-10-09 23:00 UTC)