5 ms·
Show HN: Beyond Z²+C, Plot Any Fractal
I've always been dissatisfied that simple Mandelbrot explorers proport themselves as a Fractal Graphing Calculator. In summer break between semesters, I started making a real graphing calculator, parsing LaTeX to WebGL to let you graph most any combination of z and c.
Fun ones to try include
- sin(z^2+c)
- c^z
- z^{1.7}+c
Also supports animation, just enter any other letter and turn it into a variable. Supports Mandelbrot or Julia Set style calculation.
Use with a graphics card or integrated graphics
- mg 1y agoI'm not sure if every fractal can be expressed as an iterative formula f(z,c). In 2012 I found a fractal by using a fundamentally different approach. It arises when you colorize the complex plane by giving each pixel a grey value that corresponds to the percentage of gaussian integers that it can divide: https://www.gibney.org/does_anybody_know_this_fractal https://www.gibney.org/does_anybody_know_this_fractal
- akunzler 1y agoGood point, this site then supports every (as far as I know) fractal you make with iterations of complex numbers and constant cutoff values, mandelbrot style. There are surely infinitely many more ways to generate other families of fractals though
- akomtu 1y agoWhat's the heck is gaussian integers? I've tried to parse your article, but still confused.
- Sharlin 1y agoSimply the complex numbers where the real and imaginary parts are both integers. Eg. 0, 3+i, 123-45i, -7+8i. Same as the 2D grid of integer Cartesian coordinates.
- mg 1y agoYou can think of them as the complex equivalents to normal integers. Complex numbers have two components. If both are integers, the complex number is a Gaussian integer.
- bmacho 1y agohttps://www.google.com/search?q=gaussian+integer https://www.google.com/search?q=gaussian+integer
- zahlman 1y ago> I'm not sure if every fractal can be expressed as an iterative formula f(z,c). It's also unclear to me that every iterative f(z,c) formula will produce something visually interesting, or indeed that meets the definition of "fractal".
- badosu 1y agoYou can make a fractal out of the state graph of a double pendulum: https://www.youtube.com/watch?v=dtjb2OhEQcU https://www.youtube.com/watch?v=dtjb2OhEQcU I don't doubt there could be an iterative formula that maps to it, but I'd be very surprised.
- hoseja 1y agoIsn't that trivially an iterative formula? You know, the physics solver iterating dT after dT.
- OgsyedIE 1y agoThis was a great nostalgia trip to my days on fractalforums, before the web got much denser. I tried playing around with the settings but I was unable to reproduce the two-dimensional version of Tom Lowe's Mandelbox map, discovered in 2010: https://sites.google.com/site/mandelbox/what-is-a-mandelbox https://sites.google.com/site/mandelbox/what-is-a-mandelbox There are galleries on the other pages of the site, if anybody is interested.
- ttoinou 1y agoMy favorite alternative to Mandelbrot is the Monkelbrot, I made this 13 years ago (probably I discovered this formula on the old fractalforums.com) https://www.deviantart.com/titoinou/art/The-42-MonkelBrot-292062483 https://www.deviantart.com/titoinou/art/The-42-MonkelBrot-29... f(z) = ( (z*c-1)^2 - 1 )^2 - 1 It features Classic Quadratic Mandelbrots z^2 and also Quartic Brots z^4 in one set, that is apparently connected (I didn't prove this yet...). Also, it doesn't go crazy like others alternative, it stays nicely behaved like the original Mandelbrot set. You can copy paste "( (z*c-1)^2 - 1 )^2 - 1" without the quotes on this site to explore the fractal It's really fascinating when navigating the fractal to try to understand where would a z^2 minibrot appear vs. where would a z^4 minibrot appear
- OgsyedIE 1y agoIt is tragically the case that most of the archives of fractalforums are irretrievable and lost media. The archive.org copies are very incomplete and the database dumps, as far as my research last year could figure out, are locked behind a group of moderators of an inadequately programmed successor site who don't want to share them, considering the dumps to be a status moat for themselves.
- akunzler 1y agoThe Monkelbrot! https://www.juliascope.com/share/6876dcfda602d0a43f41b2e9 https://www.juliascope.com/share/6876dcfda602d0a43f41b2e9 Sounds like I missed out on fractalforums.com :/ oh the webpages lost to the ether
- 1y ago
- dejobaan 1y agoI like things where you can just jump into the guts and play around. If you spend enough time plinking, you can end up getting an intuitive feel for a system. Also surprised at how many iterations you can crank out these days; I once implemented a Mandel-generator on my TI-81 calculator, and that took forever. Thank you for creating and sharing this!
- mreid 1y agoAs someone who taught myself 68000 assembler as a kid in order to render Mandelbrot and Julia sets quickly it still blows my mind a little that fairly hi-res versions of these can be rendered basically instantaneously in a browser using an interpreted language.
- gerdesj 1y agoSimilar(ish) although I only really got as far as BASIC on a 80286 running DOS 3.something! I did manage to get something in C to compile and work with hard coded co-ordinates but it took me ages and didn't float my boat but it was rather faster 8) I suppose I'll always be a scripter. I had a copy of the "Beauty of Fractals" and the next one too (can't remember the name). I worked in a books warehouse as a holiday job before Poly (UK Polytechnic - Plymouth) and I think I persuaded my parents to buy me the first and the second may have fallen off a shelf and ended up in the rejects bin. I got several text books for Civil Engineering too, without even needing to cough drop them myself. One of the books had pseudo code functions throughout which even I could manage to turn into BASIC code. I remember first seeing a fern leaf being generated by a less than one screen (VGA) program which used an Iterated Function System (IFS) and I think a starter matrix with carefully chosen parameters. Nowadays we have rather more hardware ...
- mreid 1y agoI also had to convince my parents to buy me books about fractals. My prized possession as a 15 year old was a copy of Mandelbrot's "Fractal Geometry of Nature". A lot of it went over my head but it had some gorgeous colour plates and interesting sections. I still have it at home some 35 years later. That also inspired me to write IFS code for ferns, Sierpinski gaskets, and Menger sponges in 68k assembler (after realizing AmigaBASIC was too slow).
- bongodongobob 1y agoHa, same. I remember setting Fractint to render something and hoping it would be done when I got back from school.
- brandonpelfrey 1y agoA long time ago I tried a version of this (https://github.com/brandonpelfrey/complex-function-plot https://github.com/brandonpelfrey/complex-function-plot). Can you add texture lookup to yours? Escape time could map to one texture dimension and you can arbitrarily make up another dimension for texture lookup. Being able to swap in random images can be fun nice demo!
- JoshTriplett 1y agoThis is a lot of fun to play with. However, I managed to find a case where it got extremely slow. I changed z^2+c to z^a+c (a from 1..3), and it suddenly got many orders of magnitude slower.
- Eduard 1y ago> Fun ones to try include - sin(z^2+c) - c^z - z^{1.7}+c - the broken formatting confused me. - couldn't test any of these via copy and paste: c&p doesn't work at least on Chrome Android for the expression input. nevertheless: very cool. I especially love the parameter animation
- KingOfCoders 1y agoThis is so amazing, I remember running ONE frame of this realtime animation over night (getting to bed and hoping for the best) on a C64 and later it still took a long time on an Amiga (machine code both). Even learned 3D GFX from an Amiga Fraktal Book (Markt&Technik) - the only Amiga book still on my shelf.