Fibonacci and Art

Graziella Hartwig Parizotto • English Project

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The Spiral - A poem

It is the siral concept

In the sequence forget

In the mind it is kept

And in the madness it's slept

It is true? That you actually find the blue?

It is true? In the gardens that you grew?

It is true? That you were mine and nothing now?

It is true? That the spiral was all you knew?

I've never fallen from quite this high

And I know I might just die

The spiral keeps going straigh

While I fall apart twice a day

There is a shadow blue ad grey

And the spiral just goes away

We sing the golden ssequence

We find madness quite frequent

The wounds are still recent

We still need treatment

It is the siral concept

In the sequence forget

In the mind it is kept

And in the madness it's slept

It is true? That you actually find the blue?

It is true? In the gardens that you grew?

It is true? That you were mine and nothing now?

It is true? That the spiral was all you knew?

I've never fallen from quite this high

And I know I might just die

The spiral keeps going straigh

While I fall apart twice a day

There is a shadow blue ad grey

And the spiral just goes away

We sing the golden ssequence

We find madness quite frequent

The wounds are still recent

We still need treatment

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Golden Spiral

In geometry, a golden spiral is a logarithmic spiral whose growth factor is Ø (or phi), the golden ratio. A golden spiral gets wider or further from its origin by a factor of Ø for every quarter turn ir makes.

There are several comparable spirals that approximate, but do not exactly equal, a golden spiral.

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The golden spiral of Fibonacci

The Fibonacci spiral: an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling;

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Context and a little bit of history

Fibonacci numbers are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci. In his 1202 book Liber Abaci, Fibonacci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths.

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Discoverying the Fibonacci Sequence

The Fibonacci numbers, commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1.

F0=0, F1=1 and Fn=Fn-1+Fn-2 for n>1

and the sequence starts:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 35, 55, 89, 144, ...

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Junji Ito - Uzumaki 1998-1999 (spiral)

In this image, Junji Ito shows the madness that growns upon the father of one of the protagonists. In the story Uzumaki (trans: spiral) the concept of the spiral takes the city of Kurôzu-cho, a fictional city of Japan.

I really like how Junji Ito works his way of making the simple concept of a spiral can take a whole town to madness.

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Front cover of Junji Ito's Uzumaki vol. 2 1998-1999 (spiral)

The cover of Junji Ito's Uzumaki (trans: spiral) is, surprisingly colorful, contrasting with the black and white pages of the work. The autor always make sure to present Uzumaki as a Cosmic Horror, since he has influences coming from H.P. Lovecraft. And this is very appreciated.

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Junji Ito - Uzumaki 1998-1999 (spiral)

The meaning of the use of spirals is a mistery during the whole reading, but as the story goes on, Junji Ito explores on how the simple idea of the spiral can take a toll on the minds of the habitants of Kurôzu-cho (fictional city in witch Uzumaki takes place).

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Junji Ito, the artist behind Uzumaki (1998-1999) taking a selfie in a spiral staircase.

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Junji Ito - Uzumaki 1998-1999 (spiral)

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Fibonacci sequence in art as Vincent Van Gogh's Starry Night (De sterrennacht) - 1889

I always admired Vincent Van Gogh, for his art and for all the struggles he had passed during his life time. How he could translate his pain and his agony through tick layers of paint.

Is admirable how even when he couldn't deal with his feelings he let art express his emotions. He uses drastic colors and impulsive brushtrokes to mask his own insecurities.

It is know that during his life time, Van Gogh had many psicotic and delirious episodes, and I can empatize because I suffer with Paranoid Schizofrenia, and I kwon how pscicotic and delirious can take a toll in someone's life.

Van Gogh also indulges in self destructives behaviors, like alcohol abuse and self harm. I also indluge myself in self destructive behaviors and in self harm, and even though I don't think anyone deserves to suffer from it, the pain of Van Gogh is translated into the canvas.

Van Gogh also spent some time hospitalized in various psychiatric hospitals and so did I. Something that will always be with me is the knowledge that the experiences I had in psychiatric hospitals tainted me forever, and I think it mark him too.

It was in one of his stays in the Saint- Rémy-de-Provence, that he painted the famous "Starry Night" (De sterrennacht) - 1889. In all the times I was hospitalized, I wrote poetry, and it was a way to deal with things.

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The golden ratio

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Fibonacci sequence as The Great Wave of Kanagawa by the artist Katsushika Hokusai in 1820-1831 from the Ukiyo-e period in Japan

The woodblock print, "The Great Wave of Kanagawa", depicts a swell of water that appears to engulf not only the boatmen delivering fish to the city of Edo - today's Tokyo -, but even the mount Fuji.

Big waves, earthquakes and tsunamis are part of the japanese cultura, suck as tropical florest are for Brazil. for the japanese people, the concept of big waves is much more close to home, and this is why this depicture of is so famous in and out of Japan.

The japanese people accepts the waves in their most primal way, they undersand that waves anre unpredictable, that in one minute they're there and the next minute they're gone.

The artist - Katsushika Hokusai - had an ability to capture waves in all variety, and returned to the subject again and again over the course of his career, from 1790 until his death in 1849. He was the artist who put together the drama of man and nature oviked in "The Great Wave of Kanagawa".

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Fibonacci sequence as a shell.

When i was little, I always asked myself how could a shell have such a beautiful shape, such an unusual style. The Spiral. Growing up, I had even more interest on how could this specific shape is on so many diferent types of shells, shells of different animals. But looking through the perspective of science and nature, the shells clearly follow the Fibonacci sequence. Is the equations evoking the most beautiful thins in nature.

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Double Fibonacci sequence as a spiral galaxy

Space. The Universe. Galaxies. The world(s) among us and the mysteries they hold. The spiral galaxies can be looked from the perspective of the Fibonacci Sequence, if you put two spiral next to each other, they will create a vortex that resembles the sipral galaxy.

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Fibonacci sequence in nature

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Junji Ito - Uzumaki 1998-1999 (spiral)

Why Spirals?

When did the concept of spirals became the object of study? Junji Ito's work Uzumaki can tell you a bit about how the concept of the spiral con became powerful and have meaning over the course of time. Katsushika Hokusai's "The Great Wave of Kanagawa" can show you how to use the Fibonacci Sequence in art, connecting the dots between the art and the equation. The siprals in the sky of the Starry Noght of Vincent Van Gogh tells you how madness can find its place in someone's life and chance perspectives. Actually, even nature can show you the beaty of evoking the Fibonacci sequence into it's glorious visuals.

Why Spirals?