[HN Gopher] Show HN: Beyond Z2+C, Plot Any Fractal
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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
Author : akunzler
Score : 56 points
Date : 2025-07-15 18:24 UTC (4 hours ago)
(HTM) web link (www.juliascope.com)
(TXT) w3m dump (www.juliascope.com)
| mg wrote:
| I'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
| akunzler wrote:
| Good 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 wrote:
| What's the heck is gaussian integers? I've tried to parse your
| article, but still confused.
| Sharlin wrote:
| Simply 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 wrote:
| You 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 wrote:
| https://www.google.com/search?q=gaussian+integer
| zahlman wrote:
| > 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".
| OgsyedIE wrote:
| This 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
|
| There are galleries on the other pages of the site, if anybody is
| interested.
| ttoinou wrote:
| My 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 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 wrote:
| 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.
| ttoinou wrote:
| Yeah I was sad about that
| dejobaan wrote:
| 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!
| mreid wrote:
| As 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 wrote:
| 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 ...
| brandonpelfrey wrote:
| A 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!
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