http://people.csail.mit.edu/jaffer/Marbling  
Mathematical Marbling 
Marbling refers to painting techniques for creating a stonelike appearance or intricate flowing designs.
Marbling originated in Asia more than 800 years ago and spread to Europe in the 1500s, where it was used for endpapers and book covers.
To the right is a detail from a marbled necktie from Chena River Marblers. Some other sites with marbled images are:
My webpages are about generating marbling designs mathematically.
Jürgen Gilg and Luque Manuel have collaborated to create the pstmarble package on CTAN.org which lets you create your own mathematical marblings using LaTeX.
http://pstricks.blogspot.com/2018/09/themarbledpaperwithpstricks.html show nice examples of marblings you can create with pstmarble.
You can now create pstmarble designs online! The first tutorial (about the nonpareil pattern) is Mathematical Marbling HowTo.
A paper I wrote with Shufang Lu, Xiaogang Jin, Hanli Zhao, and Xiaoyang Mao has been published by IEEE:
Lu, S.; Jaffer, A.; Jin, X.; Zhao, H.; Mao, X.; ,
"Mathematical Marbling,"
IEEE Computer Graphics and Applications
Nov.Dec. 2012 (vol. 32 no. 6) pp 2635
ISSN: 02721716
http://doi.ieeecomputersociety.org/10.1109/MCG.2011.51
Jiayi Xu, Xiaoyang Mao, Xiaogang Jin, Aubrey Jaffer, Shufang Lu, Li Li, Masahiro Toyoura,
Hidden message in a deformationbased texture,
Vis Comput
(2015) 31: 1653.
doi:10.1007/s003710141045z
Our papers about solid marbling:
Shufang Lu, Xiaogang Jin, Aubrey Jaffer, Fei Gao, Xiaoyang Mao,
"Solid Mathematical Marbling",
IEEE Computer Graphics and Applications
vol. 37, no. 2, pp. 9098, Mar.Apr. 2017, doi:10.1109/MCG.2016.42
Shufang Lu, Yue Huang, Xiaogang Jin, Aubrey Jaffer, Craig S. Kaplan, and Xiaoyang Mao.
Marblingbased creative modelling.
Vis. Comput.
33, 68 (June 2017), 913923.
DOI: https://doi.org/10.1007/s0037101713963
The fluiddynamics of short strokes:
Aubrey Jaffer,
Oseen Flow in paint Marbling (pdf),
arXiv:1702.02106 [physics.fludyn]
Blake Jones has done some righteous coding, creating a GPU
implementation of this algorithm which executes so fast that it
renders the marbling from arbitrary stylus movements interactively
in real time! The first
video on his
Turing clouds
webpage shows the system in action.
In November 2017 I presented a talk on the "Physics and mathematics of marbling" at the Isaac Newton Institute for Mathematical Sciences (in Cambridge UK). A video recording is at http://www.newton.ac.uk/seminar/20171128111011501. The slide pack is here.
Performed some experiments trying create vortexes in physical marbling. Read about it on my blog.
Aubrey Jaffer,
The LambOseen Vortex and Paint Marbling (pdf),
arXiv:1810.04646
Worked out the mathematics of Spanish wave and Turkish moire marbling! For details read:
Aubrey Jaffer,
Pigment Transport in Paint Marbling (pdf),
 
 
 
 
 
 
 
 

Fractals?
The Mandelbrot set and related curves display banding, but have only a couple parameters affecting them. These couple parameters change disparate features throughout the image. Although one can affect the drawing, one cannot control it.
Also, fractals' selfsimilarity down to infinitesimal scales is more akin to the Horned Sphere counterexample than to the simply connected homeomorphisms explored here.
So I thought until trying to create a Karman vortex street in a real marbling tank. But the "mushroom" patterns that emerged have smaller mushrooms inside of them. In the photograph, I have outlined mushrooms at 3 different scales (click for larger image).
I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.
My actions and comments do not reflect in any way on MIT.  
Geometry  
agj @ alum.mit.edu  Go Figure! 