#Sierpinski triangle

[verdantachillean]

The 4 horsemen of mathematics to pass the time

[oneefin]

inspired by a convo we had on the puzzle hunt discord

option a: 1 4 6 4 1

option b: 1 4 5 4 1

option c: 1 4 4 4 1

option d: 1 4 10 4 1

option e: 1 1 1 1 1

option f: 1 4 1

[origamancy]

Cringetober day 16: objecthead

Their name is Sir Pinski haha

[publicopinionrp]

For having zero area, this triangle sure is large

[theabandonedgarden]

[ibmathsresources]

Using matrices to make fractals

Using matrices to make fractals We start with a triangle ABC, with coordinates 𝐴(0,0) , 𝐵(1,0) , 𝐶( 0,1) as shown above.  We can this triangle F_0 and we then write this as the following matrix: We then have the following algorithm to generate the next triangle F_1. In effect this means that the triangle F_1 is made by combining the coordinates from F_1a, F_1b and F_1c.  So we now need to know…

[arbieroo-art]

SierSierpinski OverOverlap Whilst there are three smaller copies of the original each containing three smaller copies of the original and so on, the copies overlap slightly. The image is generated by a kind of random walk. At each step, the position moves toward one of the outermost corners. Which one is chosen randomly with equal probability of each outcome. Usually, the distance moved is half way from the current position to the corner chosen. This gives a perfect Sierpinski triangle. In this case I have changed the fractional distance moved if either of the bottom corners is chosen. Instead of dividing the distance by 2, I divide by 1.6. (It's still divide by 2 for the top corner.) This not only creates the overlap but also a reduced likelihood of the steps appearing as you descend the outer triangle. This reduced likelihood is replicated in each smaller copy of the whole.

[venturama]

Natural spinner

[nvskyprospekt]

helen the distortion 🌀

[blake447]

So in case anyone's following and seen my work with dragon and koch curves, and was curious about sierpinski's triangle, it can be represented with these sequences but unfortunately the process is more irregular so we cant pull the same tricks with binary sequences, at least in any manner that is immediately obvious.

Pictured above is a process where you double each element of the sequence, and pick a number to inject smaller triangles into, then repeat the process. With a bit of practice you can draw an eularian path that forms a sierpinski triangle.

If you wanna get really fancy you can vary the edge you break into smaller triangles each iteration, though its really, really hard to do on the fly

This is one i've always wanted to write a program to generate.

[mythtiide]

i think falke and adler doing that couple trend where they paint their nails the color of their partners eyes would be so cute but the problem is is that they have the same eye color 😭

[smile-files]

two quick edits: sierpinski's star of david!

i love doodling sierpinski's triangle, and it just occurred to me that the jewish star, being made of triangles itself, could be created using sierpinski's triangle :)

[ketrinadrawsalot]

Sierpinski snowflake

[the-pea-and-the-sun]

favorite shapes?

oh man.. i rly like star-shaped things like patches an jewelry an stuff w star motifs. unless u mean like geometrically in which case i fuck w a sierpinski triangle. and of course well. theres squares. that ones a classic

[publicopinionrp]

Back at it again with doing some fractals in Geometry Nodes, this time the simple classic: the Sierpinski Triangle.

[curlytrek1701]

Prof: the homework isn't that hard

The homework: