Phi & Mandelbrot Set Master Key?

[Archaeoastronomer (Archi)]

Phi can be 1,618 or Phi and five Φ = 5 ^ .5 * .5 + .5
https://www.goldennumber.net/five-phi/

The shapes this creates through Sacred Geometry starts with either a Golden Spiral or Pentragram:-

https://www.goldennumber.net/phi-mandalas/

https://en.wikipedia.org/wiki/Golden_spiral

It would be nice if we had one shape that all shapes fit as a master key including the Dodecahedron, Which Plato thought were the "bones of the Cosmos", or the energy lines of the Cosmos.

It is fairly easy to get a dodecahedron, by placing two opposite Pentacles 36 degrees apart to see the 3D dodecahedron at its centre, shown below:-

 

The Decagon, Decile, quintile and bi-quintile are related.

Thid shape comes up in DNA as shown roughly below:-

Picture below shows how the human body can be drawn using the decagon in advanced sacred geometry:-

I'll continue tomorrow.

 

Edited November 12, 2022 by Archaeoastronomer (Archi)
spelling

[Nungali]

Butterfly eggs and plankton skeletons ;

 

  

 

 

Fun with septagrams ;

 

 

 

and just for fun - down the microscope ;   'Antarctic Landscape '  

 

 

( High resolution Vitamin C  crystal )

[Lairg]

It may be better to ask what Intent generates such numerical and geometric patterns (antenna)

[Nungali]

"better"   ..... than what ?

[Archaeoastronomer (Archi)]

Hi Lairg,

This is complicated, and will take some time to show my work.

Hi Nungali, i liked the pictures!

About the humble Quintile i can only leave some poetry, however i don't know the author:-

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!

Where we can have a problem with a shape that all components fit together is The Golden Spiral, i'm looking for something that fits like a glove:-

https://www.goldennumber.net/nautilus-spiral-golden-ratio/

https://www.goldennumber.net/beauty/

To give a clue to do this, i thought i would show an illusion, with orbit patterns between the Earth and Venus which is retrograde motion, it appears that if you put this on a graph it looks like the orbit shows a pentacle and a heart, links below:-

https://www.skyscript.co.uk/venusrose.html

 

Keep this in your mind, as i move on to the Mandelbrot Set, i'll continue later.

[Archaeoastronomer (Archi)]

Now the thumbprint of god or the mandelbrot set is a fractal that appears during breaking down numbers, however although it keeps showing it self in visual math, you cant get inside it appears as a black circle and heart or kidney bean shape:-

Now look at the Mandelbrot Set shape below that also produces a heart:-

 

 

https://en.wikipedia.org/wiki/Mandelbrot_set

 

You can watch a visual math interpretation below:-

 

[Lairg]

I agree with Pythagoras that the numbers are alive.  When I used to build mathematical models of economies, numbers would get upset with poorly constructed equations.

 

If numbers are alive then I suspect geometry is also alive

 

 

[Archaeoastronomer (Archi)]

Hi Lairg,

But is Phi and the Golden Ratio/Fibonacci numbers related to the Mandelbrot Set?

 

It is by method below, but i may be able to show a better way:-

 

It is about making a double or mirror image, two opposite pentagrams that are opposite each other make a decagon, so we have to have a mirror image of the Golden Spiral to start with:-

 

[Archaeoastronomer (Archi)]

Now we have to explore a CARDIOID or an ENVELOPE CARDIOID, but it does need the right amount of envelopes.
If you scroll down link below to Envelope Cardioid you may get an epiphany moment, as the envelopes cut through the inner circle at ten points, which is what you need to fit in two opposite Pentacles 36 degree's apart:-

https://mathworld.wolfram.com/Cardioid.html

You should get an Envelope Cardioid like below:-

How to draw a fractal pentagon is below that is a image of Phi:-

I'll continue later.

[Archaeoastronomer (Archi)]

To fit all aspects of 5th Elements, Harmonics and Mandelbrot Set into one shape, although the inner and outer circle is different, we can do this with an Envelope Cardioid, graph below:- Any questions?

[Archaeoastronomer (Archi)]

Before i broke my spine i was able to meditate on this and produced the drawing below, however i am a bit weird, i hope you like it:-

[Archaeoastronomer (Archi)]

Hi Lairg,

I found one of your quotes:-

" In my experience, the logos/god of this solar system is a god of love, as is the logos of this galaxy. "

Perhaps you are right, for if this is true, then its avatar is a Cardioid or heart shape, the symbol for love, LOL!

[Nungali]

10 hours ago, Lairg said:

I agree with Pythagoras that the numbers are alive.  When I used to build mathematical models of economies, numbers would get upset with poorly constructed equations.

 

If numbers are alive then I suspect geometry is also alive

 

 

 

 Better than what ? 

[Daniel]

In my world, mandelbrot is a cookie.

 

I learned something new today, thank you.

[Archaeoastronomer (Archi)]

Hi Daniel,

It isn't proven, but some scientists think that the Cosmos is a Dodecahedron:-

https://physicsworld.com/a/is-the-universe-a-dodecahedron/

At the other end of the spectrum, we have the report below:-

https://www.sciencedaily.com/releases/2010/01/100107143909.htm

As above as below!

[Archaeoastronomer (Archi)]

Plato had something to say about the dodecahedron which is below, i wonder if he was right?

 

"The dodecahedron expresses the principle of equality in all directions (that arises from the Monad, or sphere), as does all the Platonic solids.

It is associated with Aether, Spirit, Consciousness, Quintessence, or the Heavens.

Plato said of the dodecahedron, “There remained a fifth construction which God used for embroidering the constellations on the whole heaven.”

https://www.cosmic-core.org/free/article-51-geometry-platonic-solids-part-12-the-dodecahedron/

From a small boy i have studied the Greek masters and the Golden Radio, Sacred Geometry was my first love, later another love was Archaeoastronomy, but i had to go to astrology school to learn all the myths and legends at the Faculty of Astrological Studies.

https://www.astrology.org.uk/

So i only found something on my birth chart about 20 years ago, strangely, as i have nearly two pentacles on the aspect lines between heavenly bodies, my work on Phi seemed to show, LOL:-

 

 

[Lairg]

A couple of times in northern Scotland at midsummer staring at the sun setting at 9pm I saw the sun with flat sides.  After a bit I realised that I was seeing the sun as a duodecahedron

 

 

[Archaeoastronomer (Archi)]

Hi Lairg,

One of the starting blocks of Sacred Geometry is the Versica Piscis, which does show in space, he is watching us LOL!

https://en.wikipedia.org/wiki/Vesica_piscis

 

God's eye nebula

[Archaeoastronomer (Archi)]

As i like Lord of the rings this is called Sauron's Eye, evil cackle!

[Archaeoastronomer (Archi)]

The Logarithmic spiral is approx. the Golden Spiral, as quoted below:-

"

Special cases and approximations

The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (polar slope angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers. "

https://en.wikipedia.org/wiki/Logarithmic_spiral

It comes up in the Mandelbrot set, Cyclones, the arms of Spiral Galaxies, shells and many other things.

[Lairg]

When dealing with the intelligence that manifests through geometry it is better to step outside the human persona

 

 

[Archaeoastronomer (Archi)]

Sorry Lairg,

I have a Zany sense of humour!

 

[Archaeoastronomer (Archi)]

The symbol below does have a  phi attribute:-

[Nungali]

9 hours ago, Lairg said:

When dealing with the intelligence that manifests through geometry it is better to step outside the human persona

 

 

 

Better than what ?

[Cobie]

 

On 13/11/2022 at 10:51 AM, Lairg said:

… numbers are alive.  … numbers would get upset …

 

Numbers are not “alive” and cannot get “upset”, this is because numbers are merely abstract ideas.

 

On 13/11/2022 at 10:51 AM, Lairg said:

When I used to build mathematical models of economies, numbers would get upset with poorly constructed equations.

 

As numbers cannot get upset, I  assume you were the one that got upset and projected your feeling onto the numbers.