A few months ago, I created a simple real-time Mandelbrot set explorer, but it soon occurred to me that, since doubles are limited in size, I couldn't zoom in as far as I wanted.
How do people create these incredibly deep Mandelbrot zooms? Is the only solution really to either bit shift or use some multiprecision library? Is a real-time version of that even possible?
I was just watching a documentary about the insane potential of Mandelbrot set and I'm wondering if this was explored in any scifi movie or book?
I wonder why this is the case.
One is Julia set at 0.25 + 0i and the other is a fractal with the formula (C+Z)^2+Z
https://github.com/ChrisThrasher/mandelbrot
I've been wanting to learn SFML and love applied math so I wrote a program that lets you pan and zoom through the Mandelbrot set to explore all it's unique structures. The quality of the rendering is tuned for my rather old laptop so it should run relatively smoothly on anything recently released. There are knobs in the code you can turn to get more quality and resolution out of it though.
See the README for how to build, run, and control the program.
Happy to hear about any ways this could be better implemented (particularly better ways to use SFML) or interesting features you would like to see. PRs greatly appreciated.
Thanks for checking it out!
EDIT: I love all the feedback I've gotten so far! I've made a few changes based on comments.
If you do run this, I'm particularly curious what you observe for the render time (see console output) while viewing the fractal before zooming or panning. It takes about 80ms on my old 4-core laptop but hopefully it's closer to 10ms on more modern hardware.
https://i.redd.it/om5msfrcxw581.gif
This is my first post here. I hope you like it. :)
Equation used:
z = x^(2) + c*e^(in)
I see them all the time and they look cool but I don't know what they mean
Hey guys, I have created a simple web app that can generate 2D Mandelbrot and Julia set fractals by changing different parameters.
Please give it a try and share your thoughts.
You can also download the generated fractal images.
Application link:
Mandelbrot and Julia Set Generator (shishirbhandari.github.io)
Sample image:
Unfortunately images are not allowed on this subreddit for some reason?? So I guess I'll post a link: https://i.imgur.com/InxgrqZ.png
For instance, what if the exponent is i or 2i or 1 + 2i? Does it still look like a fractal?
Now that desmos is touring complete, I'm finally able to iterate the Mandelbrot Set more than ~10 times.I know desmos is probably not the right tool but it's definitely more fun than an actual programming language.Here's my first try: https://www.desmos.com/calculator/ynzhaiiwg3
Now the problem is, that after too many iterations or if i set the resolution too high, desmos will still tell me that "definitions are nestetd too deeply", even though I don't really have any nested functions.
All I'm doing is recursively taking a number from a list, changing it and writing it back to the list.
If it get's out of range (float64), desmos will change it to 0 or infinity, but will usually still be able to use it for calculations.
Has anyone encountered the same problem when using actions?
To recreate the problem, increase either r_es or d_epth, press "Reset", then "Start/Stop".Doing that will render the Reset-button (and pretty much anything else) useless, so you'll need to reload the page afterwards.
I've read and watched a lot about the Mandelbrot set because it's super fascinating to me, but everything I've seen seems to stop just short of explaining why it's like that. I get that the bulbs are different "orbits", but then why isn't it made entirely of circles? And the antennae have the same number of "spokes" as the orbit of the bulb they're attached to, okay, but why? Why does the pattern the function makes in one part of the graph affect the shape of an adjacent part?
I've also seen lots and lots of examples of the Mandelbrot set popping up in areas you wouldn't expect it to, but every single time the video I'm watching just seems to go "isn't that a neat fun fact?" and leave it at that. But why is it there though? It clearly represents something deeper than just z^2+c, but what?
So basically I'm just asking, are there any mathematicians who are experts in the Mandelbrot set who understand why it's like that? Is there anyone who looks at it and feels like it makes sense, like they know why everything is where it is and what it means, and aren't surprised by the things they see when they zoom in? I know there are parts of math that nobody really understands yet - is this one of those cases, or is it just too complicated to sum up for a casual audience?
The split-complex numbers are defined similarly to the complex numbers, but their imaginary unit j actually squares to 1 instead of -1. (Note that the norm squared |z|^2 = z z* of such a number can be negative).
Given a split-complex s, you imagine the iterative process starting from z=0 and applying z -> z^2 + s. We say the sequence is unbounded if abs(|z|^(2)) diverges.
The Mandelbrot set is all s such that the sequence is not unbounded. Precisely which points are in the split-complex Mandelbrot set?
Bonus: for a given s, the filled Julia set is the set of starting values (alternative to z=0) for which the sequence is not unbounded. What is the relationship between the split-complex filled Julia set and the regular complex Julia set?
How come this is the case and what does this mean?
One is Julia set at 0.25 + 0i and the other is a fractal with the formula (C+Z)^2+Z
