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The Mandelbrot Set!

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Tags: Lua, Challenges, Graphics

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9 Aug, 2024 @ 10:44am

25 Aug, 2024 @ 5:25am

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What If Isaac Wasn't Isaac?

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Description

Behold, the weirdest thing I've ever made for an Isaac mod! (and trust me, there's a LOT of competition for that spot)

The mod adds a new challenge that allows you to scan across a visualization of the Mandelbrot set using keyboard controls.

Here's a few links if you're confused/curious at to what the heck this even is:
https://en.wikipedia.org/wiki/Mandelbrot_set
https://www.youtube.com/watch?v=6z7GQewK-Ks
https://www.youtube.com/watch?v=FFftmWSzgmk

Either way, it works surprisingly well, and you can zoom in a pretty long ways before floating-point precision starts to catch up with you and ruin the graph. It does run a bit slow, and I partially blame poor optimization for that, but there's also just a lot of calculations that have to be done to make the image, so it's going to be laggy regardless.

If you like what you see, maybe buy me a coffee: https://ko-fi.com/poondaedalin
(You don't have to, but if you're feeling generous, I'd appreciate it!)

18 Comments

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juegosjesica6666 7 Nov, 2024 @ 10:09am

the binding of fraactal

Poondaedalin [author] 22 Oct, 2024 @ 5:47pm

The function takes a bunch of pairs of starting pairs, then keeps squaring and adding until either it flies off to ∞, or it hits the max number of iterations (the sharpness value).

We can't just check if the number is going to ∞, but once it goes past a certain size, we can make a reasonable guess that it'll never settle to a value (I have the tolerance set to 16).

Once we have the full grid of values, we can generate a grid of white squares, then change their brightness based on how many iterations it took to fly off (or default to black if it reaches the maximum)

As for why? Well, I realized a while ago that making generic Isaac mods isn't as fun as making something completely unique and ridiculous, and I've kinda been acting on that philosophy ever since I made the Bejeweled mod last year. It's been fun so far, and I have a bunch of insane ideas that I want to try.

(I'm working on an Isaac RPG proof-of-concept as we speak

)

Poondaedalin [author] 22 Oct, 2024 @ 5:42pm

@aviess
It's not as complicated as it looks (at least I don't think it is lol):

The way the Mandelbrot set works is by taking a range of values, feeding them into a function, then repeating that process until they either settle to a value or fly off to Infinity.

The function is y = x^2 + c, where x and c are complex numbers written as (a + bi). That sounds scary, but a complex number in this context is just a pair of numbers with slightly different behavior when you multiply them together, since i^2 is -1. There's some correlation between complex numbers and rotation around a circle that makes the visualization do a lot of the crazy stuff that it does, but that's not really important for this explanation.

You can technically use any pair of numbers for c, and any other value's graph is called a Julia set, but I used (-1, 0) for the classic image.

[continued on the next post since Steam only allows 1000 characters per comment >:( ]