#mandelbrot

[cannibalcaprine]

some bits of the Mandelbrot Set :3

#doodles #fractals #mandelbrot

[dduane]

...Today's fractal. (I've had a couple hundred of these sitting around forever in my Flickr account, which I've started sorting through as I think about redistributing its contents elsewhere and closing it down.)

The best of these will probably pop up here on and off over the next couple of weeks.

#fractals #Mandelbrot

[msexcelfractal]

Mandelbrot Set: Iterations 1–9.

Displayed in Microsoft Excel by a four way circular reference:

C3=COMPLEX(C$2,-$B3) JN3=IF(JN274>=3,C274,IMSUM(C3,IMPRODUCT(C274,C274))) C274=IF($A$1,JN3,C3) JN274=IMABS(C274)

Each of the four formulas is filled into 72900 cells to make 270px images. The first grid picks a complex number c = x+yi. The second grid iterates Mandelbrot's rule: c is in the Mandelbrot set if and only if the sequence zₙ₊₁ = zₙ² + c does not diverge. The third grid makes the previous iteration's zₙ₊₁ into the current iteration's zₙ (unless the pause button is set in cell A1 - then this grid reverts to z₀ = c.) The fourth grid takes the absolute value of zₙ so I can show you its magnitude with conditional formatting!

At the top of the post is the fourth grid in iterations z₁ through z₉ with -2<x<1 and -1.5<y<1.5. The ranges for x and y are set dynamically so I can zoom into the fractal arbitrarily :)

Here are the red, green and blue locations from my earlier survey of the Mandelbrot set via its Julia sets.

Or, you can peruse the rest of my Excel fractal art.

#math #fractal #microsoft excel #my art #mandelbrot #mandelbrot set #mathblr #effort post

[fullcravings]

Milk Chocolate Walnut Mandelbread

#milk chocolate #walnut #mandel bread #mandelbrot #cookies #baking #nuts #chocolate #chocolate chunk #recipe #jewish #https://www.trufflesandtrends.com/home/2021/3/3/milk-chocolate-walnut-mini-mandelbread #trufflesandtrends

[blake447]

I realized I hadn't shared this here yet! Here's my 3D printed Quaternion Julia Set! See I first learned of these things reading about it from a pretty well known graphics programmer Inigo Quilez. Theirs are a lot prettier! But yeah, if you're familiar with Julia Sets and the Mandelbrot set already, this is basically that but we use 4D complex numbers called quaternions instead of the regular old complex numbers.

The original shaders I used to render them were unity CG/HLSL implementations, but this particular one is from a GLSL implementation over on my shadertoy you can find here: https://www.shadertoy.com/view/tdt3W8 It isn't exactly the same one that I've printed here (I've long lost the exact seed) but it is reasonably close. The way I printed it was I stole some marching cube code for blender and just plugged in the SDF function derived by Inigo Quilez, tweaked the values and eventually got a mesh I can print!

This uh, isn't the one I used lol. It did take a few tries to get one that was both visually interesting and also printable. In fact i wasn't even using the marching cube algorithm at first. I was using Poisson Surface Reconstruction with a python script that casted points to form a point cloud. Basically I was attempting to create a mesh like you would with photogrammetry, just with an abstract object rather than an actual thing or place.

The results were, well not good lol.

*Continues digging through box* I know its around here some where, I should have the one that works. Okay this still isnt it but this one is using the same method, I just wanted to use this for a vrchat world instead of using it for 3D printing. It gets the point across lol

But yeah. 3D printing is really cool if you're into a bit of math

#julia set #fractal #quaternion #quaternions #3d printing #math #mathematics #blender3D #mathblr #progblr #codeblr #mandelbrot #programming #coding

[spidernickelss]

miss mandelbrot :)

#mandelbrot #fractal #character design #oc art #art #digita art

[olbaid-st]

Deep Mandelbrot Set #160 Magnification = 6.39e+1078 = 2^3583.716 Max iteration = 3,697,565

#fractal #mandelbrot #fractalart #mathematics

[joshwylie]

Freaking Fractals - WYLIE - 2023

#art #artist on tumbr #fractal #fractal art #mandelbrot #rainbow #rainbow colors #gold #trippy

[myztikcloud420]

#mandelbrot #psychedelic art #dmt #lsd #visionary art #fractal art #hexagons #vivid colors

[echogene]

#mandelbrot #fractal #maths #mandelbrowser #fractal art #spiral

[politeanarchy]

working title: God Allegedly Doesn't, But I'm Not Letting That Stop Me

(enlarged to show detail)

#fractals #spirals #dice #whales #good omens #or at least good omens adjacent #mandelbrot #infinity #seven #ineffable games

[art-of-mathematics]

Do you have any recommendations for free resources like books, podcasts, videos or courses that help an autodidact get a first glimpse of chaos theory or game theory? Both topics will probably come up at my workplace and I felt you'd be a good person to ask! Thank you for your time

I'm glad you came to my ask box; Currently I do not remember most of the resources I once used, but once I remember I will reblog that post.

- Benoit B. Mandelbrot's book "The fractal geometry of nature" is pretty good for getting a good "visualized idea" of the topic of chaos theory, fractal geometry and dynamical systems. It uses helpful analogies and some parts are really awe-inspiring - overall, good food for the imagination as well!

In the meanwhile:

Does anyone of my mutuals/followers/[other humans seeing this post] know any good (introductory) resources about chaos theory and game theory?

#tarathecogsci #chaos theory #game theory #dynamical systems #fractal #fractals #mandelbrot #chaotic processes #benoit mandelbrot #the fractal geometry of nature #chaos science #fractal geometry #books #refefences #resources #math #mathematics #physics

[mrvelocipede]

Spiderwebbed Minibrot, 2015

#fractals #mandelbrot #spirograph #the great fractal retrospective of 2023

[fullcravings]

Mandelbrot Jewish Cookies

#mandelbrot #mandelbread #jewish #twice baked #cookies #food #baking #almond #nuts #recipe #cinnamon #biscoitt #rosh hashanah #hannukkah #tea time #breakfast #dessert #snack #bellyfull

[blake447]

How have I never done this before? This looks *arcane*

Basically I'm just throwing the uv's through the mandelbrot function a few times and sampling based on that. The texture isn't even like, regular or anything its a lighting bake

Eventually the NaN's start creeping in from the edges and you get this familar image

#chess #fractals #mandelbrot #shaders #mathblr #math #programming

[yourfavsmokesweed]

mandelbrot fractal smokes weed :)

YOUR FAV: MANDELBROT FRACTAL FROM FRACTALS SMOKES WEED IN A DENNY'S PARKING LOT!

#tw weed #tw drugs #your fave smokes weed in a denny's parking lot #request #anon #mandelbrot #fractal