Fibonacci Number, Phi and Mandelbrot Set.

[Astronomer]

Hi, i thought i would try to give you my observations regarding Phi, Golden Ratio, Fibonacci Numbers and The Mandelbrot Set, mostly by visual mathematics or geometry, as there is a shape that all these equations fit into that may interest.
Firstly i will start with some poetry, but i have no idea who the author was, but it made me smile:-

I am a ratio notice by few,
a pyramid, a flower, in math and in you.
A golden mediocrity in planets and space,
Fibonicci's forty in my fifteenth place.
Although quite small, i stretch to infinity,
the ancient Greeks raised me up to divinity.
Fraternities exploit me without knowing my meaning,
some people maintain i have a mystical leaning!

When i was 9 or 10 i become interested in the Greek classical philosophers like Plato and Pythagoras, so it wasn't long before fascinated by Phi and wondered if the creator was a mathematician, yet i was confused by all the shapes it produced, like a Pentagram, Pentagon, Dekagram, Decagon, and the mighty Dodecahedron, but they do fit together like a glove as shown below, the Dodecahedron shows up in 3D, latter i will explain my interest in the Mandelbrot Set and how it can be connected to the Golden Ratio:-
What do you think of diagram below showing most shapes of Phi, but not the Golden Spiral?

 

[Astronomer]

The retrograde motion orbit of Venus in how it appears from Earth traces a heart or cardioid and a rose or pentacle in the sky, however this is an illusion by both the Earth and Venus traveling at different speeds in orbit around the Sun:-
www.youtube.com...
Please note i am very interested in the black cardioid/heart that you can't see inside of in the mathematical fractal of the visual Mandelbrot Set:-
www.youtube.com...
All these shapes can be confusing:-
Golden Ratio:-

Golden ratio - Wikipedia

en.wikipedia.org

But the Golden Spiral can confuse, but can fit the pattern, when looking at the "Thumbprint of God" and the Mandelbrot Set:-

Golden spiral - Wikipedia

en.wikipedia.org

The Mandelbrot Set - "Thumbprint of God"

 

[Astronomer]

Logarithmic Spirals are approx. related to the Golden Spiral that we see in nature with shells, Spiral Galaxies, plants and Cyclones:-

Logarithmic spiral - Wikipedia

en.wikipedia.org

I have always found Fractals interesting in nature and there are some mathematicians that do find close links between the Golden Spiral and The Mandelbrot Set:-

I did find some aspects of the Mandelbrot Set frustrating, for as you go through the sequence, you always come back to the heart shaped structure with a circle attached that remains black that you cant get inside of to investigate.

Mandelbrot set - Wikipedia

en.wikipedia.org

Several years past, but then fully investigated the Retrograde pattern of Venus which gave me the start of an idea, which was to double up on shapes:-
Skyscript: Venus, the Heart and the Rose by Nick Kollerstrom
To find a way to bring all the shapes of Phi together into a master key then please scroll down link below to Cardioid envelope, that has the right amount of envelopes to cut through inner circle at ten equal points:-

Cardioid -- from Wolfram MathWorld

The curve given by the polar equation r=a(1-costheta), (1) sometimes also written r=2b(1-costheta), (2) where b=a/2. The cardioid has Cartesian equation (x^2+y^2+ax)^2=a^2(x^2+y^2), (3) and the parametric equations x = acost(1-cost) (4) y = asint(1-cost). (5) The cardioid is a...

mathworld.wolfram.com

A larger image below:-

 

[Astronomer]

It is highly likely that by using a mirror image of the Golden Spiral gives us a shape of a master key involving the fifth element when fitted in an envelope cardioid

 

[Astronomer]

This link has very fascinating work involving the two pyramid structure involving mirrors and sacred geometry of humans
www.people.vcu.edu...
Advanced sacred geometry of human form below, please note drawn with two opposite pentagons.

 

[Astronomer]

Just as Plato believed that the Universe was a dodecahedron, there are astronomers that think there is some merit in this theory:-

Is the universe a dodecahedron? – Physics World

Cosmologists might have to rethink their most basic ideas about space

physicsworld.com

Golden ratio discovered in quantum world: Hidden symmetry observed for the first time in solid state matter

Researchers have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture.

www.sciencedaily.com

I'm only showing how accepted number graphs in Mathematics regarding Mandelbrot Set could be related to Phi, Golden Spiral and Fibonacci Sequence, obviously some can be more philosophical by diagrams below,the jury is out with both concepts:-

 

[John G]

Relating sacred geometry and actual math tends to be hard to follow. I have seen Ramon Lull-like figures that look similar to your dekagram and relate to Clifford algebra and you can go from there to Fibonacci numbers/golden ratio and I've seen someone go from the golden ratio to Mandelbrot/Julia sets (which oddly enough relates to Schwinger sources mentioned in the thread on Ark's videos). I tend to just stay at the Clifford algebra part.

 

[Astronomer]

Hi John G,
I tend to think all religions have a few secrets that they hide, and as i try to study all of them, i do get information that correspond, although wimsical, most religions when followed correctly view the creator as "LOVE", it would be very strange if the shape would be a cardioid or heart by visual mathematics and sacred geometry, as the symbolism of love is a heart shape.
The start of sacred Geometry often starts with the Vesica Piscis, the symbol of the fish that Christians use today comes from this geometry:-

Vesica piscis - Wikipedia

en.wikipedia.org

The Eye of Providence is connected:-

Eye of Providence - Wikipedia

en.wikipedia.org

To create an eye shape you need to use a Vesica Piscis
Actually this does happen in the Universe as shown below:-

The Hourglass Nebula

The Hourglass Nebula

www.spacetelescope.org

To add humour and being whimsical, i have added the links below:-

 

[Astronomer]

Perhaps i am drawn to this type of study, as just by using Quintile and Bi-Quintile aspects of astrology, i have pentagrams on my birthchart that i found 20 years ago.
Large planetary alignments are poorly understood in astrology, so don't even attempt to analyse.

 

[Astronomer]

Below is a geometric picture of human DNA, it is unfinished because it would have become too messy to fully see, but i'm sure you get the idea:-

 

[Astronomer]

We think of Phi as 1.618, however the equation can be shown as Φ = 5 ^ .5 * .5 + .5 many countries follow the equation and hide it in architecture, which is why, when built, the Washington Monument was 555 feet and 5 inches tall.

Number Five (5) and Phi - The Golden Ratio: Phi, 1.618

The number 5 is intrinsically related to Phi and the Fibonacci series. Phi can be derived from several formulas based on the number 5. The most traditional, based on the geometric construction of phi is this: This formula for phi can also be expressed all in fives as: Φ = 5 ^ .5 * .5 + .5...

www.goldennumber.net

Washington Monument - Simple English Wikipedia, the free encyclopedia

simple.wikipedia.org

More Phi pictures of flowers below:-

 

[Astronomer]

I found the link below very truthful about the history and symbolism of the pentagram, it has been tainted by human misinterpretation, but with everything there is dualism:-

The History and Symbolism of the Pentagram

With Halloween slowly creeping around the corner, I wanted to share with you a new post that focuses on one of the most popular symbols used in witchcraft--the Pentagram. If you don't feel like reading, you can see my video of it on my new YouTube channel, LightnDarkChat! This channel is...

www.dualcrossroads.com

It is a personal view that complete understanding of dualisn is needed before progress can be made in consciousness of spirit:-

Dualism in cosmology - Wikipedia

en.wikipedia.org

 

[John G]

It is a personal view that complete understanding of dualisn is needed before progress can be made in consciousness of spirit:-

Dualism in cosmology - Wikipedia

en.wikipedia.org

For the math of physics, Ark has in his blog been looking at the vector-covector dual:

http://courses.cms.caltech.edu/cs177/hmw/Hmw3.pdf

The Hodge dual is also mentioned in the above article. It relates to geometric/Clifford algebra and I've seen it related to physics duals like matter-antimatter, spacetime-Kaluza-Klein space, bosons-ghosts, and creation-annihilation operators. You can get duals within these duals like space-time, longitudinal-transverse space, positive-negative (color-anticolor) charge, and in Ark's version of gravity, translations-special conformal transformations.

Ark is going after consciousness via physics; you can also like with Laura's work have duals such as Service to Others (STO) vs Service to Self (STS) and physical vs spiritual which are more closely related to your link though for me it's the same vector math structure which can be plotted and will look sacred geometry-like.

 

[mbww]

Fractals are cool and the ancients were sharp and smart to figure out phi, but in order to turn sg into real insight, always remember that we're dealing with dynamic systems. Obviously, there's more than trigons and quintiles to an astrological chart as we're dealing with constantly moving bodies, and the vector precedes a certain alignment, which for our 2d representation is fine. Then there is complexity as in many elements, rocks, species and the map of Britain:). And you have to make sense and it all to zoom out. There is a concept call bifurcation diagram that stems from chaos theory, which bot influences the generation of a fractal as in Mandelbrot set and is a resultant of the preceding set, and which IMO is the closest analogy with the emergency of consciousness, as feedback property. The ancients must have had this intuition too, especially in the megalithic civilization, as they were able to form a perfect feedback machine between their emerging consciousness and the celestial dynamics, starting from simple alignments and ratios. "Blessed are the meek..."
This video gives you an idea about what I am trying to talk about.

 

[Astronomer]

Hi MBWW,
I have come here to learn as well as give my own observations, so thank you very much for your video, over the next few months i will study it in detail, it will take some thought to reply yet, but love chaos theory!
Hi John G,
I did want to get to the Hodge Star, that you show on your avatar picture, i tend to study Mundane Astrology, meaning the astrology of countries and have been interested in large planetary alignments since 2003 and the Harmonic Concordance being planets that align in Trines and Sextiles, in astrology this is called a Grand Sextile, you can read about it below:-

THE HARMONIC CONCORDANCE

These have orbs and margins so are not exact, astrologers often fight over the margins to use, however i did do some investigating for the 20th Century, and thought you may be interested in some that took place in the 20th Century, as you know some may interpret this shape as "A Star of David".
Heinrich Himmler visited Auschwitz on 1st March 1941 and ordered expansion into the evil Auschwitz-Birkenau, strangely there was an alignment on 17th March 1941, which is what astrologers call aspect patterns, this happens when planets align and involved Uranus, Neptune, Venus, Mars, Moon and Comet Chiron!
I will show the planet pattern below, information below on Himmler's visit to the area:-

Early concepts / Auschwitz II-Birkenau / History / Auschwitz-Birkenau

Strangely a Star of David configuration appeared in the sky 16 days after Himmler's visit to Auschwitz, we have to admit, it was an odd co-incidence?

The Soviet Army liberated Auschwitz on 27th January 1945, a few days after on 7th February 1945, another Star of David appeared, using Moon, Mercury, Venus, Uranus, Neptune and Pluto, over Auschwitz, it's getting spooky now, LOL!

On 27 Febuary 1948, a Star of David alignments passed over Tel Aviv, Israel, which was approx. two and a half months before the Israeli Declaration of Independence on 14th May 1948, link below:-

Israeli Declaration of Independence - Wikipedia

en.wikipedia.org

The Star of David involved Moon, Mercury, Venus, Mars, Jupiter and Uranus.
This aspect alignment did show up at all locations, however i have placed it in Tel Aviv as it is more auspicious!
Astrology graph below:-