Saturday, 5 July 2014

Fractal Atomic numbers

 
The illustration/graph compilations on this page highlite the
similarities  between features in the graphs of atomic number
vs. element conductivity.  Repeating patterns and self
similarity between small and large sections  of the original
red graph suggest a fractal element to the arrangement
of  atomic numbers and their associated properties.
Initially consider the the four highest conducting elements
(Be, Al, Cu, Ag and Au) They increase their atomic numbers
at very near the same  rate as the increase seen in the noble
gases  The increases are shown in the example below .
For instance, between Ag and Au the increase in conductivity
is 32. Note the same increase in atomic number, 32, is
seen in the noble gases between Xe and Ra...

Be(4)    Al (13)  Cu(29)  Ag (47)  Au ( 79) - best conductors
         9            16       18         32
Ne(10)  Ar(18)   Kr( 36)  Xe (54)  Ra (86)  - noble gases
         8           18        18        32
 
In the illustrations supplied the original graph of element
conductivity vs atomic number is in red. Overlayed in the
illustrations are graphs of various repeating patterns. These
graph sections are taken from the original red graph and
either placed size as in different parts of  the illustration
or enlarged or reduced and repositioned onto the red graph
to show similarities in profile.
In the first illustration these samples are labelled as sets
1 to 5 in the table below. For instance, sets 3,4 and 5 show
how the main peaks in the red conductivity graph between
Calcium (20) and Copper (29),  are in fact a repeating
pattern found in other parts of the red graph.
Also, set 1 shows how the section from the  main red graph 
between Be (4) and Ag (47) , once enlarged , very closely
matches that of the section in the main red graph between
Be (4)  and  Au (79).
In the second illustration a section from the red graph up to
atomic number of Ag is stretched to 2 different sizes and
re-overlayed onto the red graph to show how a fractal element
can be seen in small and large sections of the red graph

 
 
Set 1
Be  Ca  Cu  Ag  Au
4    20   29   47  79
matches
Be  Al   Ca  Cu  Ag
4    13  20   29   47
Set 2
Cu  Rb  Mo  Ag
29  37   42   48
matches
Ca  Cr  Co  Cu
20  24  27   29

REPEATING PATTERNS...
Set 3
Ca  Cr  Co  Cu
20  24  2 7   29
matches
Be -     Na   Al
4    -     11  13
Set 4
Ca  Cr  Co  Cu
20  24  27  29
matches
Rb  Mo  Rh  Ag
37   42  45  48
Set 5
Ca  Cr  Co  Cu
20  24  27  29
matches
Yb  W  Ir    Au
70  74  77  79