I 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!
Show HN: Beyond Z²+C, Plot Any Fractal
11–20 of 29 posts
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#12I'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
> 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".
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#13As 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.
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#14As 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.
Similar(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 ...
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#15My 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-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 ot…
It 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.
Yeah I was sad about that
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#16A long time ago I tried a version of this (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!
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#17My 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-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 ot…
The Monkelbrot! https://www.juliascope.com/share/6876dcfda602d0a43f41b2e9
Sounds like I missed out on fractalforums.com :/ oh the webpages lost to the ether
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#18As 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.
Ha, same. I remember setting Fractint to render something and hoping it would be done when I got back from school.
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#19This 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.
Re: Show HN: Beyond Z²+C, Plot Any Fractal
#20I'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
You can make a fractal out of the state graph of a double pendulum: 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.