marble-dyed fabric

Mathematical Marbling

marble-dyed fabric

Marbling refers to painting techniques for creating a stone-like 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 web-pages are about generating marbling designs mathematically.

J├╝rgen Gilg and Luque Manuel have collaborated to create the pst-marble package on which lets you create your own mathematical marblings using LaTeX. show nice examples of marblings you can create with pst-marble.

You can now create pst-marble designs online! The first tutorial (about the nonpareil pattern) is Mathematical Marbling How-To.

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 26-35
ISSN: 0272-1716

Jiayi Xu, Xiaoyang Mao, Xiaogang Jin, Aubrey Jaffer, Shufang Lu, Li Li, Masahiro Toyoura,
Hidden message in a deformation-based texture,
Vis Comput (2015) 31: 1653.

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. 90-98, Mar.-Apr. 2017, doi:10.1109/MCG.2016.42

Shufang Lu, Yue Huang, Xiaogang Jin, Aubrey Jaffer, Craig S. Kaplan, and Xiaoyang Mao.
Marbling-based creative modelling.
Vis. Comput. 33, 6-8 (June 2017), 913-923.

animation of short stroke

The fluid-dynamics of short strokes:

Aubrey Jaffer,
Oseen Flow in paint Marbling (pdf),
arXiv:1702.02106 [physics.flu-dyn]

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 The slide pack is here.

Performed some experiments trying create vortexes in physical marbling. Read about it on my blog.

real-time animation of vortex exponential-time animation of vortex The animation on the left shows several seconds of the decay of a Lamb-Oseen vortex. The animation on the right shows the decay with exponential growth of time. For details read

Aubrey Jaffer,
The Lamb-Oseen Vortex and Paint Marbling (pdf),

Nonpareil wrapped onto cylinders Worked out the mathematics of Spanish wave and Turkish moire marbling! For details read:

Aubrey Jaffer,
Pigment Transport in Paint Marbling (pdf),

virtual paint marbling The Mathematics of Marbling
serpentine marbling Serpentine Marbling
paint marbling Scallops and Clams
marbled torus Marbling the Torus
curved banding Textile Designs
rolling marble Transfer Effects
marbling Dropping Paint
pattern-welding Pattern Welding
spiral marbling Gallery


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' self-similarity 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).

See blog post for more information.

Copyright © 2003, 2004, 2006, 2007, 2010, 2011, 2016, 2017, 2018, 2019 Aubrey Jaffer

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.

agj @
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