How I made my own Fractal

You didn’t make one fractal, you’ve made infinite families of fractals.

That's pretty interesting, this is like a fractal that you can infinitely zoom out on instead of infinitely zooming in on. One thing I've noticed is that the level 2 one is actually just rule 150, the 1D cellular automata, which is "one of the eight additive elementary cellular automata" according to Wolfram and as a result, it's already fairly well studied. Looking at Rule 150 might give more insight to the family itself.

I remember being obsessed with Conway's game of life and trying to make a 1D version of it on a spreadsheet (with time progressing on the vertical axis). In doing so I accidentally discovered rule 126 (if three adjacent cells have a sum of 1 or 2, then the center cell underneath has a value of 1, otherwise it has a value of 0) and created a Sierpinski triangle, which pleased me greatly. I assume it's a specific case of your class of fractals, and follows the same rule as your n=3 instance at 4:17. For those wanting to replicate it, in LibreOffice Calc, you can paste the formula =IF(OR(SUM(A1:C1)=1,SUM(A1:C1)=2),1,0) in the B2 cell and drag the formula across the whole sheet (don't drag it on the col A and row 1 though, leave those empty), and write 1 in any cell in the first row. It's particularly fun to see the patterns it builds when you have more than one full cell in your initial conditions.

I invented with same fractal about 8 years ago a different method. Its cool to find someone explore and re-discover/ also found this fractal

This was super interesting! I wonder if that has already investigated before. If not, I'm definitely rooting for the term Kuvina Triangle! You obviously put a lot of work in these videos, and the content is really good. I'm kind of amazed that you put this video out so quickly after the last one checks channel 13 days ago. This is severely awesome ^^ All the best to you! Hope you have fun, and don't overwork yourself. <3

Heya, I came up with this 2 years ago! Cool that someone else thought of it independently, though I took it a bit farther in a different direction. This isn't really a 2d fractal, or well it is, but it can be thought of as having 1 spacial dimension and 1 temporal. I use 2 spacial and a time dimension. There is a defined list of "neighbors", and between each update each cell will add itself to all its neighbors. Some especially pretty ones are the neighbors being knights moves, and having it reach in all 8 directions!

i have a weakness for these kinds of explorations. amazing video kuvina!

I saw you in 3blue1brown's comment section, not gonna lie I dont regret coming here.

The basis for this fractal is the trinomial triangle, so named because the terms of each row correspond to the coefficients of expansions of trinomial expressions. I independently discovered this when trying to figure out how to describe the outputs of the probability distribution of rolling 3 dice, then found there's already a body of research on it, from Euler to Wikipedia! I love your variations of it, and I particularly like how the fractal for n = 127 looks like it has cool sunglasses on, and how product 48 makes the pan flag. You might also be interested in Rule 90 and other related 1D cellular cellular automata. I spent a while nerding out about these.

I found this while watching TV. I do not regret it. Very underrated and well done!

level 5 and 7 are beautiful but my favorite one has to be 29 127 looks like a static triangle with triangle sunglasses

Since each composite triangle is a composition of its factors, you could theoretically use this for encryption

These are so cool! I also really love the lesson at the end of, if you have something, tweak and change it to see what happens. I still remember sometimes where I was trying to solve something, and that tip helped so much. Also to answer your question: My favorite is Product 30

a lot of the prime fractals there look like they could make for great noise generation! Like especially when you look at one corresponding to 107, you can already see how it is incredibly irregular, looking like some sort of fog! I like it very cool

I liked level 3 and any variations on it :)

26 is neat with the isolated color also 27 with the sorta inverting green and blue halves

All of the multiples of 17 are beautiful

7:55 cool glasses tho 13:14 THE GAY SEED

(16:09) Fun fact: I once saw the number 103 in a dream. It was the age rating of a movie that my parents were watching on Netflix.

The fact that there are distinct triangles mage out of squares is amazing