SnowFlake

Von Koch

 

 

 

 

 

 

 

   Artistic Concept:

 

Oil 7 – SnowFlake ( of Von Koch [1870-1924] )

2008 - ( 40 x 40 cm )

 

   Scientific Concept:

 

     A journey through ever-smaller scales shows us the increasing complexity of continuous reproduction of triangles emerging from a single central equilateral triangle and where it overlaps with this triangle another one in the same way and with the same area but with an inverted position, thus obtaining a six-pointed star. Each of these points is a new equilateral triangle, and again it is repeated the same method we used on the original triangle. We will obtain a continuous range of split ends again divided in new smaller triangles and so on, continuing indefinitely this building process up to infinity. Only the change of scale may reveal the existence of this hidden order of repetitive patterns, consisting of smaller and smaller triangles, nearly invisible, imperceptible at first glance.

     Helge von Koch was a Swedish mathematician, who gave his name to this geometrical fractal, becoming known as 'Koch Snowflake' or simply as 'Koch Curve'. In this work he intended to bring together methods of elementary geometry and related them with the theory of curves. In this new model of scientific invention, the imagination plays a key role, contradicting the imperturbable calm of scientific logic.

     Being fractal geometry the branch of mathematics that studies the properties and behavior of fractals, this new geometry was able to describe many situations that could not easily be explained by classical geometry, such as the attempt to measure the size of this object through the settings based on traditional Euclidean Geometry. Certain fractals, formerly known as 'monster curve', define geometric objects that can be subdivided into parts and each one of which always has similarities to the original object, composing scales with endless details, presenting default patterns repeatedly. In this particular case, if we apply the classical functional relationship between the variables Perimeter and Area to ​​the Koch's Snowflake, we note that although the area of ​​the Von Koch Snowflake is finite, the perimeter, however, is infinite!

 

 

    Literary Concept:

 

“I feel that I am born every moment to the eternal newness of the world.”

FERNANDO PESSOA

 

“Take the spirit of my spirit to the future.”

- ‘When Nietzsche wept’ -

IRVIN YALOM

 

“Projecting time in Eternity.”

ELIADE

 

“I may not rise to great heights, but I will climb alone.”

CYRANO DE BERGERAC

 

“The impossible also happens. It only takes a little longer.”

ALDINA ROCHA

 

“Chance favors only the prepared spirits.”

LOUIS PASTEUR

 

“Start by doing what is necessary, then what is possible;

and suddenly, you'll be doing the impossible.”

S. FRANCISCO DE ASSIS

 

“Hope is the dream of the waking man.”

ARISTOTLE

 

“The finest qualities become useless when the power of character and personality does not sustain them.”

THÉOPHILE GAUTIER

 

“A warrior knows that the ends do not justify the means.

Because there are no ends;

there are only the means.”

- ‘Manual of the Warrior of light’ -

PAULO COELHO

 

“Seek not to hide anything; time sees, hear and reveals everything.”

SOPHOCLES

 

“And do not forget who you are,

at the time you find yourself surrounded by what you are not.”

N. D. WALSCH

 

“It's good to have an end to the journey, but in the end,

 it is the journey that counts.”

 URSULA LE GUIN

 

“The objective is the path itself.”

STEFAN KLEIN

 

“ The way of life is doing and being at all moments.”

LAO-TZE