#sierpinski fractal

[art-of-mathematics]

Wobbly Sierpinski-fractal model/toy

Made with foil strips of equal length and book screws.

The larger triangle at the center is stable because the outer tinier triangles stabilize it. (The larger triangles have a side length of two foil strips. The smallest triangles ("the building blocks") have a side length of 1 foil strip. The largest triangle is this entire model with side length of 4 foil strips.)

The largest triangle (4foil strips) is stable, because the tiniest (1foil strip) triangles stabilize each other as well as the larger (2foil strips) triangle.

The sierpinski pattern has interesting properties regarding its "stability" I have to admit.

Normally I struggle to make equilateral triangles of side length "2 foil strips" stable enough without adding an inner triangle. This construction (using outer tiny triangles) is a good solution if you want a "larger triangle hole".

[nvskyprospekt]

helen the distortion 🌀

[violetfractal]

I used excel to generate some 3 dimensional analogues of the Sierpiński gasket, then constructed the outputs in Minecraft :D

These fractals are embedded in 3D space, but they are not themselves 3 dimensional:

The diorite structure (left) has fractal dimension log_2(5) ≈ 2.3 (since each unit consists of 5 subunits at 1:2 scale).

The granite structure (right) is built from 4 half-scale copies of itself, so bizarrely its dimension is log_2(4) = 2.

As a consequence of its low dimension the 16x16x16 structure has a volume of just 16^2 = 256 blocks. The other fractal, also 16x16x16 but 2.3 dimensional, has a volume of 625. That’s beefier than the 2D one, but a solid 16x16x16 3D cube would dwarf it with V = 4096.

Finally, since this blog is msexcelfractal and not msminecraftfractal, here’s the formula and blueprints I used for the 2.3D structure.

Original Date: June 9th, 2023 9:56pm

[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.

[knotty-et-al]

1st iteration of the Sierpinski Tetrahedron - with an octahedron at the center.

The octahedron serves as "core".

Attached to that octahedron core are 4 tetrahedra.

Modules used: 24

[ 12 for the octahedron, 4x3 for the 4 tetrahedral tips ]

If I attach 4 more tetrahedral tips - so that all faces of the octahedron are stellated - it would turn into a stellated octahedron/stella octangula.

[notfarts]

Hi I saw a demo by Héll Mood and wanted to try coding it on javascript myself :3>

It's kinda slow (bruteforce-raymarching-over-a-3D-array slow) but it's fun to explore randomly generated sierpinski-like sponge fractals.💮 Move with arrow keys, hold shift to go faster.

Credit where credit's due, this was made by closely trying to visually replicate the original demo Atlantis, by Héll Mood.

I learned a lot about ray marching, math, algebra, fractals, and some crazy bs about javascript. Weak typing is chaotic, can't believe the best way to force integer division is to use double bitwise not operator like ~~(a/2)

Anyway hope you like!

[ketrinadrawsalot]

Sierpinski snowflake

[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 :)

[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

[curlytrek1701]

Prof: the homework isn't that hard

The homework:

[origamancy]

Cringetober day 16: objecthead

Their name is Sir Pinski haha

[art-of-mathematics]

4 Tiny Tetrahedra assembled together to one Large(r) Tetrahedron. (incl. octahedron-shaped gap at the center)

(Hand for scale)

Today's Tiny Tetrahedron

(artist of the colorful artwork in the background of the first photo is unknown)

[theabandonedgarden]

[tilbageidanmark]

(From)

[blake447]

One more lol. Sierpinski Eulerian circuit, colored based on distance along the circuit. Ended up fairly visually interesting

[draconym]

Good morning and happy new year. It seems that the content of most of his drunk texts (which he told me not to look at) was "choosing a different polyhedron to gift to each friend based on vibes and/or math puns."

My wonderful spouse, who I love very much, set a phone alarm to remind him to send drunk texts to his friends this evening, and ensured that he would be appropriately drunk (0.086%, currently) by consulting a blood alcohol calculator that factored in change over time. He was worried that this level of planning was against the spirit of Drunk Texts, but I assured him it was not.