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Show HN: Beyond Z²+C, Plot Any Fractal

juliascope.com

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Re: Show HN: Beyond Z²+C, Plot Any Fractal

#21

Post by ttoinou »

akunzler wrote: post #17
ttoinou wrote: post #7

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 ot…

The Monkelbrot! https://www.juliascope.com/share/6876dcfda602d0a43f41b2e9 Sounds like I missed out on fractalforums.com :/ oh the webpages lost to the ether

Hehe, I missed the sharing feature thanks.

IIRC it was a user named monk who found a method to generate any Monkelbrot set containing our customized choice of any z^n brots

I found the (2,4) pair the most beautiful

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#22

Post by mreid »

gerdesj wrote: post #14
mreid wrote: post #13

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.

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 jo…

I 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).

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#23

Post by Eduard »

> 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

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#24

Post by KingOfCoders »

This 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.

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#25

Post by progmetaldev »

bongodongobob wrote: post #18
mreid wrote: post #13

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.

Ha, same. I remember setting Fractint to render something and hoping it would be done when I got back from school.

I spent many hours experimenting with Fractint, trying to get the inner and outer coloring just right, along with the zoom magnification that I could handle walking away from the computer for long enough to get something interesting. The worst was zooming somewhere that looked interesting, and coming back many hours later to find out you had nothing of value.

I spent my early teen years addicted to Fractint, before I could even really show off my creations except in person to my friends. I still look back at those days as more interesting with computers than now. Maybe I need to go back and write my own software to render fractals (or work on existing fractal software and see if I can improve it). In the mid-2000's, I was using GnoFract4D to render fractals, and the results were far more impressive. A change in GNOME or Ubuntu created an issue with the render window for me, and I ended up abandoning it.

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#26

Post by bravesoul2 »

mreid wrote: post #13

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.

It might be JITed not interpreted though

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#27

Post by hoseja »

badosu wrote: post #20
mg wrote: post #2

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

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.

Isn't that trivially an iterative formula? You know, the physics solver iterating dT after dT.

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#28

Post by pabs3 »

akunzler wrote: post #17
ttoinou wrote: post #7

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 ot…

The Monkelbrot! https://www.juliascope.com/share/6876dcfda602d0a43f41b2e9 Sounds like I missed out on fractalforums.com :/ oh the webpages lost to the ether

https://www.fractalforums.com/ is still online but read-only, but there is also a new forum at https://fractalforums.org/

I just queued an ArchiveBot job to save fractalforums.com to archive.org too.

Re: Show HN: Beyond Z²+C, Plot Any Fractal

#29

Post by pabs3 »

OgsyedIE wrote: post #10
ttoinou wrote: post #7

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 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.

fractalforums.com seems to be online still, so I just queued a recursive ArchiveBot job to save fractalforums.com to archive.org.
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