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   Patterns XL v1.1

Create Colorful Visual Art using your Math Skills!

Patterns XL for iPad is a 2D graphing calculator to create an infinity of colorful image patterns from mathematical expressions of arbitrary complexity. It can help students improve their math skills by developing some visual intuition of 2D mathematical expressions as function of Cartesian (x,y) or polar coordinates (r, theta). Using Patterns XL graphic designers can also create fancy icons or illustrations, and vision scientists can recreate their favorite visual stimuli for publication purposes or create new ones right from their iPad without any need for scientific desktop software like Matlab or Mathematica. For the iPhone & iPod touch version: check out "Patterns" here.

Multiple expressions with quasi-unlimited number of variables can be combined to produce simple or complex patterns. Pattern images can be saved to the device's Photos Album at various resolutions, and their formulas can be exported through email with embedded previews. A list of favorite patterns can be also stored for later editing or archival purposes.


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Each mathematical formula, z = f(x,y,r,theta), describes the gray or color components (z, zr, zg, zb) of the pattern as function of Cartesian or polar coordinates. Find below some beautiful examples created using the iPhone version of Patterns. The exact same expressions can be used on the iPad version.

Contrast Basics: Luminance modulation along each axis (x, y, r, theta)

Combining Axes before and after the Modulation

Color Basics: simply replace contrast z in [-1,1] range by brightness zr, zg, and zb in [0,1] range

Patterns for Vision Scientists


Version 1.1 (March 5, 2014):
- Compatibility with iOS 7

Version 1.01 (December 20, 2010):
- Fix a random crash when dismissing photo-album or email export popover,
- Fix the email export size setting not being properly saved in the app preferences.

Version 1.0 (December 19, 2010):
- first released version on AppStore.