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
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
https://sites.google.com/site/mandelbox/what-is-a-mandelbox
There are galleries on the other pages of the site, if anybody is interested.
https://www.deviantart.com/titoinou/art/The-42-MonkelBrot-29...
f(z) = ( (z*c-1)^2 - 1 )^2 - 1
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
Sounds like I missed out on fractalforums.com :/ oh the webpages lost to the ether
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
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 ...
That also inspired me to write IFS code for ferns, Sierpinski gaskets, and Menger sponges in 68k assembler (after realizing AmigaBASIC was too slow).
- 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
mg•9h ago
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•8h ago
There are surely infinitely many more ways to generate other families of fractals though
akomtu•8h ago
Sharlin•8h ago
mg•8h ago
Complex numbers have two components. If both are integers, the complex number is a Gaussian integer.
bmacho•7h ago
zahlman•6h ago
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•3h ago
I don't doubt there could be an iterative formula that maps to it, but I'd be very surprised.