In the interest of transparency of background for this article, you should know that I, Roy Alexander, have a patent that makes the Alexander Arrangement of Elements possible. Some say that periodic tables should not be patented. I disagree. I feel that patents in general advance science and industry, and that the periodic table should be no exception.
Invention can be in a Eureka Moment or as a result of extensive study and labor. Without some hope of compensation, the process will be abandoned. The person with a sudden idea will forget about it unless he has great resources for getting to the market first, and the plodder will never make the effort. Fewer technical advances will be made, many will be abandoned or hidden.
Patents provide the exclusive rights which usually allow the inventor to use and exploit the invention for twenty years from the date of filing of the patent application. Through these exclusive rights, he is able to prevent others from commercially using his patented invention, thereby reducing competition and establishing the inventor in the market as the correct and pre-eminent player.
Without this protection, a larger firm could quite easily take the idea and ramp up production in a fraction of the time of the inventor, taking the market, and leaving the inventor with nothing to show for his creativity.
The inventor - with a patent - now has an opportunity to produce, license, or sell the invention to another enterprise which would be a source of income, and an incentive or further invention. Consider if Edison had stopped at one idea!
Some wonder if obtaining a patent on a variant of the periodic table will stop others from doing academic research on it. That is not the case at all, research on patented subject matter for strictly academic purposes is not an act of infringement. The patent laws are aimed at preventing infringement in a commercial context. Academic and other research institutions, generally speaking, remain free to build upon patented advances.
There are three requirements an invention must meet to be patented: Utility, Novelty, Nonobviousness. Also, it must be the intellectual creation of the inventor, not that of another person.
The invention must be useful. This requirement focuses on the difference between a "discovery" and an "invention".
The invention must be different from that which already is publicly known or available.
And finally, the invention must not have been, at the time of the invention, obvious to a person of "ordinary skill" in your field. An invention which solves a problem probably is not obvious if others attempted to solve the problem but failed. A good case can be made if your invention yields surprising, unexpected results.
Many innovators have developed periodic tables which are chemical element displays different from the well known Mendeleev periodic table. Several have been devised purely for didactic reasons as not all correlations between the chemical elements are effectively captured by the standard periodic table.
Below, by Fernando DuFour, for whom "A third dimension [for the periodic table] is not an option but a necessity", is his product, called the ElemenTree. It maintains the horizontal and vertical symmetry inherent in the periodic table to relate the electron configurations of the elements to their chemical and physical properties. He holds a patent for highly informative and technical spiral version of the PT.
Roy Alexander has patented an expanded de Chancourtois spiral, using it with all the new elements. The dimensionality eliminates the confusion and apparent inconsistencies in the current flat table by permitting arranging the elements contiguously and continuously without disturbing the accepted group and property interrelationships (bottom, left side).
He and others have arrived at similar conclusions, which provide greatly improved educational tools.