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This continues the saga of the chaotic dualists, their struggle now repositioned.

In this instance new formulæ were arrived at and put through the same process as before to produce new escape-time diagrams. (The logic statements have been changed but may not be accurate)

The possible fundamental two statements might be:
X : Y is true
Y : X is as true as X is false

Notwithstanding the logic, the dynamics are formularized as follows:
x <= 1 - |y|
y <= 1 - |x - (1 - x)|

The escape-time diagram is generated from this pair. In this instance the center of the escape-time diagram plots at (0.5,0.0)


circular escape-time Gallery
Circular Escape-Time Diagram 1

A comment: Might this be the escape time diagram of the chaotic dithering where one person says, " Yes, you can," and the other says "I can't make up my mind"?

Further tinkering with the logic via the formulæ pairs can produce some interesting if not bizarre escape-time diagrams.

escape-time Gallery
Linear Escape-Time Diagram 2
 

The above diagram extends forever without limit as there is no resolution.

The dynamics are formularized as follows:
x <= 1 - |y|
y <= 1 - |x|

The time-escape diagram is generated from this pair of formulæ, which appear to exhibit schizophrenic behaviour. In this instance the center of the escape-time diagram predictably plots to (0.0,0.0)

Perhaps it could be likened to the logic of someone insisting that the other is always right, with the respodent insisting that the converse is the case. Two people meeting at a door with both saying "No! But I insist, after you." A contradiction without resolution that goes absolutely nowhere forever. Perhaps mathematical schizophrenia..?


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