Frondi-what? – A Core Concepts Guide

Throughout the content you will find at frondity.com there are continuous references to various concepts and themes, from the mathematical to the philosophical. In this section we aim to provide a bit more clarity on aspects of the content. If there is something you would like to have better reference for just let us know at admin.com

At the heart of frondity is the idea of a fractal universe. The frond is like the “leaf” of a fern. Barnsley was able to use a few simple mathematical processes to create the fractal form of a fern. Key to the processes were ideas of “randomness”, sets, probability, measurement-dependent action, and repetition or iteration. Outcomes are:

geometrical form,
all the properties of fractals
similarity through length scales
infinite geometry
sets and subsets
results of instantaneous measurements which appear random but are normally distributed when measured in large numbers
if each point is measured in terms of histogram of angles from the origin a Gaussian or normal distribution type curve is produced

This near Gaussian type curve or more specifically a Tracy-Widom type distribution is a representation of the data in one less dimension than it is more completely expressed as the fern
Many of the features of the system play into factors we understand as key to quantum mechanics
The data can form the input for a secondary fern production as a “random” set.
That iterative function systems appear to have a close relationship with fractal form
When Einstein said “God does not play dice”, with “randomness” as per its dictionary definition at the core of quantum physics, perhaps he was right
Our universe is an iterative function system
We are fractal and we live in a fractal universe
The universe may not be a frond or even slightly frondly but the fern at least makes a good and sensible analogy for us to carry out thought experiments.
For example, if the universe were fractal and the result of an ever evolving iterative function system wouldn’t we see normal distribution curves everywhere in nature and not know why…. until now that is.
Perhaps things are slightly more determined or determinable by assessing nature in these terms than by existing standard techniques.
In a universe of iterative function systems must everything be evolved? Yes must be the conjecture
If we can move through conjectures are numbers and mathematics the result of iterative function systems producing fractals? Yes would be the likely answer
What are the first principles for such a universe? A fractal form is good because similarity and difference are expressed in a single form from the first iteration through n+1.
In a world of nothing does the act of creating something in a measurable field (where reference to a former position or state is possible) necessitate a fractal form from the get go? Yes would be the likely answer
Does the previous conjecture offer any useful guide for the origins and development of the early universe? Perhaps!
Does the idea of an electron mapping out a fractal form as against a probability distribution or cloud carry more value? It must.
Does a fractal universe have useful connotations for you day-to-day? Absolutely!

We will get to other important factors in our understanding of the principles of a fractal universe or frondity as time goes on and your input as always would be very welcome. Contact admin@frondity.com for more information. Or simply contribute or question in the relevant forums linked below. Thanks for your support.

It’s worth getting a feel for the following concepts. The aim of @frondity is to promote discussion on the relevance of and relationships between sample topics like these and items in the second list. All within the context of an iterative function fractal universe (IFFU)

Artificial Intelligence
Barnsley’s Fern
Chaos Theory
Distribution
Entropy
Fractals
Geometry
Heisenberg
Iterative Function Systems
Jeopardy
Kanban
Linearity
Multiverses
Nanotechnology
Origins
Principles Vs Laws
Quantum principles
Reality
Set theory
Tree diagrams
Universe
Ven diagrams
Will (free)
X-ray diffraction
You
Zero

It is contended here that the principles of iterative function systems and their fractal output have a huge role to play in the furthering of understanding in physics and particularly the perceived boundary between quantum and classical physics.

If you have something to question or say about the relationships between iterative functions, fractals and any of the following please reference (#) the subject matter in your comments.

Quantum Physics

Addition of complex numbers
Addition of vectors
Amplitude
Annihilation operators
Anti-Hermitan operator

Antisymmetric eigenfunctions
Apparatus (measurement)
Associative property
Atoms
Average
Axioms
Basis if simultaneous eigenvectors
Basic vectors
Bell’s theorem
Boolean logic
Bracket notation
Bra vectors
Canonical momentum
Cartesian coordinates
Cartesian representation of complex number
Cauchy-Schwarzenegger inequality
Change in classical physics
Change and continuity
Change both unitary and incremental
Classical entanglement
Classical equations and quantisation
Classical limit
Collapse of the wave function
Column vectors
Commutation relations
Commutative property
Commutator algebra
Commutators
Commuting variables
Complex conjugate
Complex numbers
Complex vector spaces
Component matrices
Component form
Composite observances
Composite operator
Composite state
Composite systems
Composite vectors
Conservation of distinctions
Conservation of energy
Conservation of overlaps
Continuity
Continuous functions
Correlation
Creation operators
Crystal lattices
Degeneracy
Density matrices
Determinism
Dirac delta functions
Distributive property
Dot product
Down states
Dual number systems
Eigen-equation
Eigenfunctions
Eigenstate
Eigenvalues
Eigenvectors
Einstein
Electric current
Electromagnetic radiation
Electromagnetic waves
ElectronsSchrodinger
Energy
Energy levels
Entangled states
Entanglement
Euler-Lagrange equations
Expectation values
Experiments
Feynman
Forces
Fourier transforms
Frequency
Functions
Fundamental theorem of quantum mechanics
Gaussian curve
Gaussian function
Gaussian wave packets
General Schrödinger equation
General uncertainty principle
Gluons
Gram-Schmidt procedure
Graviton
Ground states
Hamiltonian operator
Hamiltonian equations
Harmonic oscillator
Harmonic oscillator energy level ladder/tower
Heisenberg Uncertainty Principle
Hermite
Hermite polynomials
Hilbert
Hilbert spaces
Hooke’s law
Hydrogen atom
Identity
Identity operator
Inner products
Integrals
Integration by parts
Kets
Kinematics
Kronecker delta
Kronecker product
Kronecker symbol
Lagrange equation
Lagrangian
Law of evolution
Least action principle
Linearity
Linear motion
Linear operators
Liouville’s theorem
Locality
Lowering operators
Machines
Magnetic field
Mathematical concepts
Matrices
Matrix elements
Matrix multiplication
Matrix notation
Maximally entangled state
Maxwell’s equations
Mean value
Measurables
Measurement
Minimum-uncertainty wave packets
Minus first law
Mixed states
Momentum
Momentum basis
Momentum operator
Momentum representation of wave function
Motion of particles
Multiplication
Near singlet state
Negation
Neutrino
Newton’s law
Newton’s law- the quantum version
Nonlocality
Non relativistic free particles
Normalisable functions
Normalisation
Normalised vector
Number operator
Observables
Observations
Operator method
Operators
Orthogonal basis vectors
Orthogonal states
Orthogonal state-vectors
Orthogonal vectors
Orthonormal bases
Outer products
Overlap
Parameters
Partial derivatives
Particle dynamics
Particles
Particle-wave duality
Path integrals
Pauli matrices
Phase ambiguity
Phase factors
Phase indifference
Photons
Planck’s constant
Poisson brackets
Polarisation vector
Polar representation of a complex number
Position
Position representation of wave function
Potential functions
Precession of spin in a magnetic field
Principle of least action
Principle of stationary action
Probabilities
Probabilities replaced by probability densities
Probability and entanglement
Probability and wave function
Probability amplitude
Probability function
Product states
Projection operators
Propositions
Pure states
Quantisation
Quantum abstractions
Quantum electrodynamics
Quantum field theory
Quantum Hamiltonian
Quantum mechanics
Quantum Sim
Quantum spins
Quantum states
Quantum systems
Quantum tunnelling
Quarks
Qubits
Raising operators
Real numbers
Reversibility
Row vectors
Schrödinger
Sets and Boolean logic
Simultaneous eigenvectors
Singlet state
Space of states
Speed of light
Spherical coordinates
Spin
Spin components
Spin operators
Spin-Polarisation Principle
Spin states
Spring constant
Standard deviation
State
State-labels
State of a system
State space
State-vectors
Statistical correlation
Subset
Sums
Symmetric eigenfunctions
Systems
Tensor products
Tests for entanglement
Time
Time dependence
Time-dependent Schrödinger equation
Time derivatives
Time-development operator
Time-evolution operator
Time-independent Schrödinger equation
Trace
Trajectories
Transposing
Triangle inequality
Triplet states
Truth-value
Two spins
Two-spin system
Two-state system
Uncertainty
Uncertainty principle
Unitarity
Unitary evolution
Unitary matrix
Unitary operators
Unitary time evolution
Unit matrix
Unit vector
Unit operator
Up states
Vector addition
Vectors
Vector space
Velocity
Vent diagram
Wave functions
Wavelength
Wave packets
Waves
Wheeler
X-axis spins
Y-axis spins
Zero function
Zero

Frondi-what? – A Core Concepts Guide

Share this: