# Notes on structures of binary trees

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A Project Proposal
Algorithmic detection of a determinance signature within presumably pure random data events

## Introduction

A binary tree is built by adding to a list a sequence of data elements as numbers or characters representing something that can be compared to previous event values within the list.

The list element also stores pointers to other positions in the list. A binary tree is built such that each list member points to the next greater list member occurrence, and the previously lesser list member occurrence. A full explanation of binary trees and their many varieties and treatments is beyond the scope of this project proposal. (See Binary tree at Wikipedia.org.)

## Scope of Points of Significance About Binary Trees

• An outcome of random data that is graphed into a tree is that a balanced tree is produced, meaning the length of most outer nodes fall within an average distance from the root node.
• Number of nodes linked on a left link from the root node will be very near the same number on the right link from the root node.
• The more random events added to a binary tree there are, the more balanced the tree becomes.
• A catena (a sequence of pre-ordered, non-random events) may occur within random data.

## Conjectures

• A presence of catena (a pre-ordered chain, or linked list) within a binary tree will increase if the randomness of the data events is influenced by a determinance acting upon the data source.
• A catena occuring early in the data event history will have more effect of the evolution of the tree than a catena occuring late in the tree's event history.

## Considerations for Testing of Conjectures

• Pseudo random data is cyclic, and as such will create a skew from randomness.
• Cyclicities within a random data stream are a determinance created by the algorithms producing the random data.
• Pure, random data (if such really exists) might be sensorized as pulse events by:
• Conditioning the ground floor noise of electrical current.
• Conditioning the pulses produced from radiative isotope emissions impinging a PIN diode, which pulses are nuclear events.
• Conditioning the pulses within Zener diode reverse current, which pulses are created by quantum tunneling events.
• Data logs of various natural events may serve as pure random data.
• Pure random data may be used as a tare value for conditioning cicuits (adjust determinance detection algorithms to indicate zero determinance).
• Pseudo random data may be used to adjust detection algorithms for determinance skewed data.
• Algorithmic detection of determinance from logged data is just as effective a live data for testing and calibration.
• Trichel Pulses exhibit memory that prolongs indefinitely as a state-change from pure randomness.
• The influence upon the potentially random pulse amplitude and inter-pulse timing of a Trichel pulse chain is a detectable determinant that would be measurable by the project proposed.

## References

Stochastic Properties of Trichel-Pulse Corona Physical Review A, American Physcial Society