Thursday, 26 December 2013

Fourth-Order Magic Torus Chart

The fourth-order magic tori have already been identified and classified by type in a previous article "255 Fourth-Order Magic Tori, and 1 Third-Order Magic Torus." The fourth-order magic tori have also been indexed in numerical order using normalised squares for convenient reference in the "Table of Fourth-Order Magic Tori."

The latest study below shows how the 255 4th-order magic tori are linked, and how they interrelate. The Fourth-Order Magic Torus Chart proposes the division of the 255 magic tori into 25 groups, and indicates the position of each magic torus in the system. All of Bernard Frénicle de Bessy's 880 4x4 magic squares, and all of Henry Dudeney's 12 square types are accounted for. A sample page of the Fourth-Order Magic Torus Chart is shown here:

Fourth-order magic torus chart sample page

New development!

Posted on the 21st January 2018, an article entitled "Multiplicative Magic Tori" shows that the 255 magic tori of order-4 are different multiplied states of 82 Multiplicative Magic Tori (MMT) of order-4!

Although it is outdated by "Multiplicative Magic Tori," the Fourth-Order Magic Torus Chart continues to represent previous research, and is still available below. Please note that if you click on the button that appears at the top right hand side of the pdf viewer, a new window will open and full size pages will then be displayed, with options for zooming.

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