The Valence Shell Table of Elements

In 2007, while working with Eliav Eini on some of the groundwork for this site, we noticed the emergence of the odd number line, in broken form, while counting the number of valence spaces in different elements on the periodic table of elements.

The first version of the table was made using paper, tape and scissors and has sat in a journal for 6 years. 

The reordering of the periodic table breaks the physical continuity of the periods and sees each series ended by a noble gas. Informationally, the periods are maintained by colour.

I find that this reorganization presents a highly ordered description of the elements and their interrelated stability.

Driving this reorganization was the observation that the available spaces in sequential valence shells was given by a somewhat fractured representation of the odd number line, f(n)=2n-1, where the total number of spaces per shell divided by 2 is represented by the sequences:

1, 3
1, 5, 3
1, 7, 5, 3 

The Printable version is available here: periodic_table.png

This is the table:


Thermodynamics, Number Theory and The Goilden Ratio
Creation, Evolution and the Golden Rule
Theory of Order
Why Fibonacci and Gibonacci sequences appear everywhere in nature,
and how simple combinatoric math can describe how a Universe with simple beginnings evolved into a complex form