#julia set

[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

[picturesquephysics]

From Quanta Magazine's article: "3-D Fractals Offer Clues to Complex Systems".

#julia set #fractals #maths #mathematics #science and art #nature #language of the universe #universe #source #infinity #physicsblr #mathsblr #studyblr #geek

[lucyofthelunarrealm]

these are some things i found when exploring some julia or fatou sets and the mandelbrot set, using my own little program.

most of these are from various julia or fatou sets of the function c*sin(z) for different seed values. the others are from the classic z^2 + c.

#mandelbrot #julia set #mathematics #math art #fractal

[msexcelfractal]

Julia3.xlsx is a 13 Mb Excel 2010 spreadsheet that generates 16 successive iterations of f(x)=x^2+z on the complex plane at 128px resolution. You are watching Julia sets grow!

The code for this spreadsheet turned out surprisingly simple:

A2=COMPLEX(A3, A4) B1=COMPLEX(COLUMN(B1)/32-63/32,ROW(B1)/32-2) DZ1=IMSUM($A$2,IMPRODUCT(B1,B1)) B129=IMABS(B1)

The Mandelbrot Set is the set of z-values for which the Julia set is connected. Because the above Julia set is disconnected, .3-.01i is not a member of the Mandelbrot set.

I chose z-values close to the boundary of the Mandelbrot set so that my Julia sets would get cool spirals :)

Below is my working map of the Mandelbrot Set with the locations of my five Julias shown.

The map is in Desmos. All construction and coloring of the Julia sets was done in Microsoft Excel. Crop and add the z-values, GIMP.

Bonus: The last few iterations of each set have shrinking halos. I did not intend this behavior! The white exterior is simply the region where the absolute value of f¹⁶(x) overflows a 32 bit floating-point number:

just taking my pet $VALUE!s for a walk

#math #fractal #microsoft excel #my art #not a cellular automaton #desmos #julia set

[mndlbrt]

#looming... #fractals #julia set #grey

[anomalocariscanadensis]

#fractals #julia set

[inkydigit]

Fractal Friday-f710p

New Fractal for your visual enjoyment! (more…)

View On WordPress

#computer-graphics #digital-art #fractal #fractal art #imaginary #Julia Set #wallpapers

[maukustus]

I made a little Julia set visualization in GeoGebra with the help of Ben Sparks (youtube video)

#julia set #fractal #geogebra

[desdenova-yt]

A few years ago, I got real into making Mandelbrot and Julia set zooms...I found some of my old images! Here's some of my favs. Descriptions are in the alt text.

#mandelbrot set #julia set #fractal

[dendpj]

Tessellation of Julia Set Fractals

#creative coding #generative art #fractal art #geometry #pattern #julia set #tessellation

[fractl-art]

Autumn Colours :3

4096x2160

z^2 + -0.0570499931500625 + 0.8804277883061249i Julia Set

#julia set #render #math #chaos #fractal #background

[blake447]

Getting my arch install looking nice and pretty. Background is a quaternion julia set, and down below we have my dragon curve code that I've been working on. Finally got polybar installed and working, and customized it lightly. Next I'm thinking a compositor so i can have transparent terminals and stuff if I want

#arch linux #linux #unixporn #c programming #c #dragon curve #julia set #fractal #rice

[jkvjimin]

you're my beginning and my end, that is all my meeting and my farewell

for @raplinenthusiasts 💚

#yoongi #namjoon #hobi #kim namjoon #min yoongi #jung hoseok #bts #btsedit #bangtan #bangtan* #rap line #gif #raplineuser #userkelli #usersky #annietrack #userdimple #rjshope #tuserandi #useremmeline #usermaggie #dailybts #cr. namuspromised #hi julia 💞🌻💞🌻 #i was watching this concert with my bf and he said “wow you should make a gifset of them here” #“you have a friend who'd like it” #and he was talking about you hahahaha he's so lovely #ily julia hope this set makes you happy somehow! 💛🌻💚

[spicyclematis]

it's giving high fasyun 💅 for @raplinenthusiasts

#me making this set: why are they judging me #yoongi #hoseok #namjoon #bts #btsgif #btsedit #trackofthesoul #cypnernet #bangtan #usersky #annietrack #bts rap line #tw flashing #ofc this one's for julia like who else i can associate with #actually i wanted to use the marie claire one for yoongi but #it doesn't match namseok because it had softer concept #mygifs

[msexcelfractal]

Uploaded to Wikipedia by Maxter315:

The animation of the Julia set for the complex quadratic polynomial fc(z)=z^2+C. Values of C for each frame evaluates by equation: C=r*cos(a)+i*r*sin(a), where: a=(0..2*Pi), r=0.7885. Thus, parameter С outlines circle with a radius r=0.7885 and a center at origin of the complex plane. Created in Matlab R2011b using escape-time algorithm:A=10e6, max_iter=81. Colormap - mirrored jet(40).

A Julia set is a subset of the complex plane whose elements stay bounded under repeated iterations of a polynomial.

#math #fractal #art #not mine #julia set

[mndlbrt]

#fractals #julia set #rainbow #unhappy with these. couldnt articulate why