Hilbert Curves

Representing nearly a decade of software development and math research, Hilbert Curves is an iOS app, available in Apple's App Store, that presents to the math-curious person an electronic book, entitled Outside-In and Inside-Gone, for the iPad/iPhone. The author and illustrator, Doug McKenna, is a longtime, award-winning software developer, fractal pioneer, and space-filling curve expert who (among others) created illustrations for Benoit Mandelbrot's The Fractal Geometry of Nature, the paradigm-shifting book that introduced fractals to the scientific world nearly 40 years ago.

Filled with interactive and animated illustrations, McKenna's book/app first explains how to understand the Hilbert Curve, one of the most elegant and important constructions in all of mathematics. The treatise then goes on to generalize this space-filling curve construction in several ways, including many new ways that have never been seen before. It demonstrates how to create space-filling curves whose borders are not just linear, but almost-everywhere linear, fractal, or even space-filling themselves.

Here is an assortment of screenshots from the app on an iPad:

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iPad Fig126

Although this app might be construed as a PDF reader, it is not. Indeed, there is no PDF in it at all. Instead, the app contains its own, high-performance TeX language interpreter, developed by the author over the course of many years, to accomplish the highest quality document and mathematical typesetting. And all illustrations are drawn by code in the app itself, many under the control of the reader/user.

Sample screenshots from the app on an iPhone:

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iPhone Fig8

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This is the first electronic book published by Mathemaesthetics. We anticipate other such books, and are looking to collaborate with authors of technical subjects that have been waiting for an electronic book platform that supports large numbers of interactive illustrations of high complexity, combined with the highest-quality technical typesetting. Let us wrap your book, written in TeX, around your interactive illustrations, or around an entire iOS application.