Pi and Various Power Sequence Spin Addresses

Below are draft charts of spin addresses for numbers and their powers. The boxes at the bottom (or end)  of each column (or row) show where the first ‘double is rolled’.    I made the following graphics by hand, but hope to have a computer on the job soon for data runs for hundreds or thousands of numbers in any given range, which should suggest how uniquely pi and its approximations tend toward infinity and eliminate any errors I’ve made.

A variety of numbers and their powers. The bar represent the minor hexagon each power lands in. The square at the bottom represents the first time a number 'rolls double'. Every number rolls double, in this sample, by 18 rolls. Pi has rolled 33 in the prime hexagon, and has yet to roll double.
A variety of numbers and their powers: rolling doubles in the prime hexagon.

In the second chart, I simply look at numbers in regular increments without regard to special numbers such as pi or e.  At this resolution, there is a peak near pi and a larger one near 2.8.  Both may be random, but the larger one is suspiciously close to e.   Note, e itself, in the chart above, is unremarkable.  I will investigate this range more closely soon.

 

A range of numbers between 2 and 4 in 0.05 increments and when they roll double in the prime hexagon. About 2/3 of the numbers have rolled double by the 7th roll.
A range of numbers between 2 and 4 in 0.05 increments and when they roll double.

In a range tight around pi, those values nearest pi itself appear to have higher roll values.

Powers of numbers around Pi in 0.001 increments roll double in the Prime Hexagon.
Powers of numbers around Pi in 0.001 increments roll double in the Prime Hexagon.

When the values approach pi on the order of 0.000001, the roll values, on average, continue to increase.

Rolling double within 0.000001 of Pi in the Prime Hexagon. The average number of rolls need to roll double is increasing, but only Pi has yet to stop rolling.
Rolling double within 0.000001 of Pi in the Prime Hexagon.