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23.3D More Pictures of Root Beings

D. When the Root Number is greater than 2

True and Bogus Root Beings 3->17

Now that we have seen what happens to our Root Beings at two and under, let us see what happens when the Root Number is greater than 2. After the following explications there are 7 pages of pictures of our Root Beings under a continuum of Circumstances as the Root Number rises from 3 to 17. It is nice to see our Root Beings in process.

4th Order Root Beings when the Root Number is 3, just a little slower

When the Root Number becomes three, the approach to their Goal, their Holy Grail, becomes slower. Already the most Past-based Root Being of this computer experiment doesnt even reach computer accuracy within 200 iterations; it only reaches about 13 digits of decimal accuracy. However it is easy to visually see that each of our Root Beings, except the False Root Being, the flat green line, steadily if slowly still approach their goal. The True Root Being still approaches most quickly. The Now-based Root Beings are just a little slower while the Past-based Root Beings are the slowest of all. The False Root Being has slightly different coefficients and is approaching a distinctly different goal. Therefore it Hits the Wall.

When the Root Number is 4, Slower Still, No More False Beings

When the Root Number becomes 4, each Being approaches their Destiny a little more slowly still. The slowest Bogus Equation only reaches 9-place accuracy after 200 iterations. The True Root Equation reaches computer accuracy quickest, after only 25 iterations.

When the Root Number is 5, the Now-based separate

When the Root Number is five, another of the Past-Based Root Beings doesnt reach 16-place computer accuracy after 200 iterations. All of the Root Beings approach a little more slowly. The Now-based Root Beings have finally separated from each other. The Now Being based totally upon the past moment, which we will call All-Now, the steady red line, begins to move more slowly than the Now Being who extends a little into the past, which we will call Almost-Now, the steady green line.

When the Root Number is 6, Three dont reach computer accuracy

When the Root Number is 6, three of our Past-based Root Beings dont reach computer accuracy after 200 iterations. The slowest only reaches 6-place accuracy. Note that the Past Based and the True Root Being all approach their Goal erratically, while the Now-based approaches their Goal steadily without wandering. However the True Root Being still approaches most rapidly even though its Path is erratic.

When the Root Number is 7, All-Now slows to level of Past-based

When the Root Number is increased to seven, the approach of the Root Beings to their Destiny is slower still. Note that All Now, the steady red line, approaches no more quickly than the best Past Being. This is a real come down for All Now. When the Number was under 7 the All Now Being always approached his goal more quickly than any Past Being.

When the Root Number is 8. Slowest at 4 Place accuracy

When the Root Number is raised to 8, the True Being still reaches relative perfection within 30 iterations. The others are slowing down. The worst only reaches 4-place accuracy within 200 iterations. And humiliation for All-Now. He is now slower that the Best of the Past and only reaches 14 place accuracy. He and his brother Almost-Now still approach their Goal from the Straight and Narrow, as opposed to the erratic approach of the rest of the Root Beings including the True Equation.

When the Root Number is 9, only Almost-Now reaches bottom

When the Root Number is raised to 9, the True Being is little changed, while only one of the rest, Almost-Now, achieves computer accuracy. All-Now is further humiliated by being confused with a lower level Past Being.

When the Root Number is 10, All-Now at 4 place accuracy

When the Root Number is 10, the True Being is unaffected, still reaching computer perfection after about 30 iterations. Not so with the rest. All-Now is second slowest, only reaching 4-place accuracy after 200 iterations. Note however that all these Beings are still steadily approaching their goal even though much more slowly.

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