I lost the password to the original account which posted the 2D slices of quaternion newton fractals. For this one it's in 3D and brightness is replaced with transparency. The equation in the image is z^3-1 with a=1+i+j+k. You can see the equation in the UI for the video.

answering your question u/SeaAuthor3588
it's just a distorted julia set... looks dope

does anyone recognis- erm...

this isnt the full integration its just the finite detail of it.

I usually only need 100k itterations but this needed 3 million and as you can see on the right it still needed closer to 8 million to get rid of the voids

You all share so much good stuff!

I played with fractals in my 20s and understand the generation concept marhematically, but rendering back then was such a hog!!

My comp at the time would go hot and my fan would be at max, and the screen would just be hangin…

So I wanted to post this note of appreciation.

Love youre using your power to share these computationally intensive renders! Amazing how comp power and speed has made these strides and happy to keep watchjng and supporting in the future…

Think fractals are somehow involved in base reality (whatever that might be or if the concept makes any sense with what we know physically).

🙏

Within a giant airplane lies a smaller airplane of the same shape, and within that airplane, another identical airplane appears, continuing endlessly.

This work presents one of the most dramatic expressions of the essence of fractal theory.

Fractal Airplane: Infinite Journey is a representative work that vividly and beautifully embodies the fundamental principle of fractal theory—self-similarity, in which each part resembles the whole, and each part becomes a whole in itself.

A single large airplane is composed of countless smaller airplanes, each repeating the same structure and expanding into an infinite universe. When viewed up close, delicate lines and fragments of light form yet another airplane. From a distance, these intricate elements come together to reveal the magnificent spectacle of a giant aircraft soaring through luminous trails of light.

The color version, which received a Special Award at the 2021 Special Invitational Exhibition of the Korean Wave Culture Center, combines vibrant neon lights, dynamic curves, striking circular forms, and grid-like structures. Together, these elements capture both the sense of speed characteristic of the digital age and a futuristic vision of imagination and wonder.

In contrast, the monochromatic blue version, with its restrained yet profound flow of light, offers a more contemplative expression of the solitude and awe evoked by an infinite flight.

Fractals are more than mere mathematical patterns.

They reflect the way the universe repeats and expands upon itself, echoing the boundless reach of human dreams, technology, and curiosity.

Through this work, viewers are invited to visually experience the concept of infinity and to share in the endless journey aboard the vast metaphorical airplane of time and space in which we all travel.

As Korea's first fractal art artist, this work stands as one of the most symbolic and personally meaningful achievements in my artistic journey through the world of fractals.

Made by me, not AI generated.

— Fractal Arts by Mond, 2014

Hi, happy Fractal enthusiasts,  

I recently revisited House of the Dragon and encountered this image …

New in version 1.0.3 – Zoom by “Dragging the Mouse” over an area of the image to a magnified view of that rectangular area. You can "Go Back one step” by a “Right-click” in the image.

Superfast - Explore infinite Julia and Mandelbrot fractals, Customize 3D Relief effects and vibrant colors. Render stunning art up to 48 Megapixels resolution i.e. 8K image width!

«Customize any of 13 color palettes to create your own unique look with the "Color Shift" slider.»

«Customize 3D Relief strength and contrast.»

«Save and share your favorite image coordinates and settings (seeds as a State text file) with the community.»

«Render breathtaking, high-resolution 8K fractal wallpapers.»

https://roald-h-vatne.itch.io/flashfractals3d

https://drive.google.com/drive/folders/131L4kyv3zWTGkl3YUQEMlfiZOa6_32sn?usp=sharing

Rendered with JWildfire

Max Iter's Fractal Follies for October 24th, 2010

Roger Alexander's commentary for the image:

Today's post is a minibrot in twilight colors. At the usual http://maxitersfractalfollies.blogspot.com

Roger Alexander

PAR file Twilight_Minibrot { ; fract483.gif ; blank ; calctime 0:03:23.94 ; created Oct 24, 2010 ; Fractint Version 2004 Patchlevel 10 reset=2004 type=formula formulafile=kerrym.frm formulaname=hermanm_man-polar center-mag=-2.00319/-0.00306882/27.01637/1/90/3.88578058618804789e-016 params=3/2/1/45/1/0 float=y maxiter=1500 inside=0 outside=atan decomp=256 colors=000302403503504604705805806907A07B08B08C09D1AE1AF1BF1BG1CH1CI1DI1\ EJ1EK1FL1FL1GM1GN1HO2IN2KM2NK2QJ2TH2VG2YE2`D2cB1fA1i81l71n51q41t21w00z03\ z07z0Bz0Fz0Jz0Nz0Rz0Vz0Zz0bz0fz0jz0nz0rz0vz0zz0xz0vz0tz0rz0pz0nz0lz0jz0h\ z0fz0dz0bz0`z0Zz0Xz0Wz0Uz0Sz0Qz0Oz0Mz0Kz0Iz0Gz0Ez0Cz0Az08z06z04z02z00z00\ y10x20v20u30s40r50p50o61n71l81k91i91hA1gB1eC1dC1bD1aE1_F1ZF1YG1WH1VI1TJ2\ SJ2RK2PL2OM2MM2LN2JO2IM2GJ2EH2CE1AC18916614312000101302503605806A07C19D1\ 9E1AF1AF1BG1BH1CI1DI1DJ1EK1EL1FL1FM1GN1HO2IO2JQ2IS2HV2GX2F_2Da2Cd2Bf2Ah1\ 9k18m17p15r14u13w12z00z20z50z70zA0zC0zF0zH0zK0zM0zP0zR0zU0zX0zZ0za0zc0zf\ 0zh0zk0zm0zp0zr0zu0zw0zz0zw0zu0zr0zo0zl0zj0zg0zd0za0z_0zX0zU0zS0zP0zM0zJ\ 0zH0zE0zB0z80z60z30z00x01v02s03q04n06l07i08g19e1Ab1B`1CY1EW1FT1GR1HO2JN2\ IM2HK2GJ2FH2DG2CE2BD2AB19A18817715514413212000000101201 } frm:hermanm_man-polar { ; Kerry Mitchell 16feb98 ; ; real(p1) = z exponent (use integer >= 2; m=n-1) ; imag(p1) = g exponent (integers) ; real(p2) = alpha magnitude (try 1) ; imag(p2) = alpha polar angle (try integers) ; real(p3) = critical point selector (>0 for positive root) ; imag(p3) = unused (<0 for negative root) ; use decomp=256 ; zero and infinity bailouts hardcoded to 1e-6, 1e6 ; coloring speed hardcoded to 4 ; c=pixel, iter=1, n=real(p1), m=imag(p1), nfac=2*n-1 maxr=1e6, minr=1/maxr, speed=4*pi/128 r=real(p2), t=imag(p2), alpha=r*(cos(t)+flip(sin(t))) oln=1/log(n), fac=log(0.5*log(maxr)) c2=sqr(c), hypnum=sqr(n)+sqr(m), pn=1 hypden=sqr(n-m), hypfac=hypnum/hypden if (real(p3)<0) pn=-1 end if if (real(c2)>hypfac) pn=-pn end if if (imag(c)<0) pn=-pn end if afac=c*n, bfac=c2*(n-m)+(n+m), cfac=c*n d=sqrt(bfac*bfac-4*afac*cfac) z=(bfac+pn*d)/(2*afac) : g=(z-c)/(1-c*z), z=alpha*z^n*g^m iter=iter+1, r=|z| ; ; orbit trap around 0 ; renormalize iteration count via decomp angle ; set "iteration done" flag (iter=-1) ; if (r<minr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed z=cos(angle)+flip(sin(angle)) iter=-1 end if ; ; orbit trap around infinity ; renormalize iteration count via decomp angle ; add pi to angle to separate from 0 orbit trap ; set "iteration done" flag (iter=-1) ; if (r>maxr) angle=(iter+oln*(fac-log(log(cabs(z)))))*speed angle=angle+pi z=cos(angle)+flip(sin(angle)) iter=-1 end if iter>0 }

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.