NURIA JUNCOSA

A MATHEMATICAL APPROACH TO ART
GEOMETRIC ABSTRACTIONS

Exposition of the different mathematical approaches I used in my artwork.
A little selection of my work from 2003 till 2010

PROJECTIONS

COMPOSITION No 14
oil on canvas - 90 x 120 cm - Nuria Juncosa - 2010

COMPOSITION No 13
oil on canvas - 4x100x100cm - Nuria Juncosa - 2010

'Embeded Solids' (quadtych)

From the series studies on projections of polyhedra in to a two-dimensional plane.
Partial projection of a tetrahedron in to a dodecahedron in to a Icosahedron.

COMPOSITION No 12
oil on canvas - 70x70cm - Nuria Juncosa - 2009

This painting is a symmetric composition of a partial projection of an tetrakis hexahedron.
In geometry, a tetrakis hexahedron (also called a disdyakis cube) is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated octahedron. It can be seen as a cube with square pyramids covering each square face.

COMPOSITION No 11
oil on canvas - 90x90cm - Nuria Juncosa - 2009

Partial projection of an Triakis tetrahedron.
In geometry , a triakis tetrahedron is an Archimedean dual solid, or a Catalan solid.
Its dual is the truncated tetrahedron.
It can be seen as a tetrahedron with triangular pyramids added to each face.

COMPOSITION No 10
oil on canvas - 90x90cm - Nuria Juncosa - 2009

Asymmetric composition of an hexahedron

COMPOSITION No 9
oil on canvas - 80x80cm - Nuria Juncosa - 2009

Asymmetric composition of an hexahedron

COMPOSITION No 8
oil on canvas - 4x60x60cm - Nuria Juncosa - 2009

A composition of four canvas depicting a double inverted symmetry.
The four canvases put together refers to a pentagonal dodecahedron.

COMPOSITION No 7
oil on linen - 60x60 cm - Nuria Juncosa - 2009

This painting is a partial projection of a wireframe deltoidal icositetrahedron.
A deltoidal icositetrahedron is a dual polyhedron which looks a bit like an overinflated cube which has all of its edges bisected. The 24 faces are deltoids. The short and long edges of each kite are in the ratio 1.00:1.29.

The deltoidal icositetrahedron is a crystal structure formed by the minerals analcime and garnet.

After painting the projection of the Deltoidal Icositetrahedron wireframe on the canvas, I took the artistic freedom of creating new subfaces, occupying complementary locations by colouring up the spaces obtained by the intersections of the wireframe.

This painting took part at the Exhibition of Mathematical Art part of the Joint Mathematics Meetings of The American Mathematical Society & Mathematical Association of America
January 13-16, 2010 - San Francisco, California.

Organized by: The Bridges Organization: art and mathematics

COMPOSITION No 6
oil on linen - 60x60 cm - Nuria Juncosa - 2009

Symmetric composition of a partial projection of an icosahedron in to a two-dimensional plane.

COMPOSITION No 5
oil on linen - 60x60 cm - Nuria Juncosa - 2009

Asymmetrical composition of partial projection of an tetrahedron in to a two-dimensional plane.

COMPOSITION No 4
oil on linen - 60x60 cm - Nuria Juncosa - 2009

Abstraction of a projection of an hexahedron in to a two-dimensional plane.

COMPOSITION No 1
oil on linen - 84x84cm (diagonal) - Nuria Juncosa - 2009

Abstraction of a projection of an hexahedron in to a two-dimensional plane

ROTATIONS

This series of paintings, it really started when thinking about the line as two-dimensional object and
its movement in the space when applied symmetry.

Before I made the composition with the four oil paintings, I made dozens of pen drawings in black and/of red ink , pointing to rotational symmetry in the two-dimensional plane,

I gived most of this drawings away during the ARS GEOMETRICA convention in Pecs, Hungary

One of this drawings was exhibit during the exhibition about the Line at the Fény Galeria in Budapest during the symmetry Festival organizated by the International Mobile Madi Museum Foundation and the SYMMETROLOGY FOUNDATION

"3, 4 and 5-FOLD ROTATIONAL SYMMETRY"

(Quadtych)
oil on linen - 168x168 cm (diagonal) Nuria Juncosa - 2009

PROPORTIONALITY

PHI

ASTROIDS

FIBONACCI SPIRAL

A Fibonacci spiral is created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling.

The painting "Prostration"is a tilling with squares whose sides are successive Fibonacci numbers in length.
In this painting I use canvases of sizes 10cm, 10,cm, 20cm 3ocm, 50cm and 80cm.
Each number is the sum of the previous 2 figures.

POLY- SPIDRON

The spidron is a spiral-shaped figure, made up of triangles.

It was first modeled in 1979 by Daniel Erdely and later developed by Amina Buhler-Allen and Marc Pelletier.

The figure itself is a plane-filling tile, but when folding it can also create a three dimensional object that completely encloses an area.

CURVES

The next series of paintings are on curves.

A curve is a mathematical concept, which in generally a non-straight line is indicated.

THE CURVE OF AGNESI

ASYMPTOTES

The term asymptote is derived from Greek asymptotos and means literally "not falling together".

In mathematics, an asymptote is a straight line continually approaching a curve but never meeting, as they go to infinity.

The constructed forms reaches or extends beyond the canvas, forcing the viewer's attention to a specific direction.

ALGEBRAIC STRUCTURES

In a new approach, to create artwork I use algebraic structures in order to obtain patterns.

To carry out the artistic designs I can use different variables: Additive or multiplicative structures, module, shapes, color, shapes of the table, geometric transformations like symmetries, rotations, translations to make tessellations, etc

At this point I'm ready to substitute each numerical symbol by all kind of geometric or organic figurations, in the corresponding table and I can use the numeric relationships to highlight different geometries in order to obtain artistic designs!

MAGIC SQUARES

DIVISIBILITY

In a new approach, in the painting T100m9, in order to create the patterns I divided the canvas in 100 squares corresponding to the numbers 1 till 100.

Number 1 and most of the another prime numbers are painted in black. Number 2 is also a prime number but because I have to determine a colour, I painted in red. Here after, all the numbers divisible by 2 are painted in red. Number 3 is also a prime number but for the same reason I painted in yellow, here after all the numbers divisible by 3 are painted in yellow. Numbers divisible by 4 are painted in green. Number 5 is also a prime number but I painted in light blue. Numbers divisible by 6 are painted in red dark blue. 7 is also a prime number and I painted in magenta. Numbers divisible by 8 are painted in violet and numbers divisible by 9 are painted in orange.

In the painting The Cherubs of Thaumaturge Apolonius, I divided the canvas in 16 squares corresponding to the numbers 1 to 16 and I visualized all the numbers divisible until 5.

Number 1 is a geometry. Number 2 is a baby. Number 3 is a pacifier. Number 4 is a potty but because number 4 is divisible by 2, the baby sits on the potty. Number 5 is a teddy beer, number 6 is divisible by 2 and by 3,  therefore the baby sucks the pacifier, etc

LINEAR PATTERNS

In the series Ruimtelijke Ordening, to create patterns I used tables (m, k) with two variables: the module m and the columns k.
This patterns changes when there is a variation in the module m or in the column k.

Once established the matrix, I substituted de numerical symbols by organic and/of geometric figurations in the corresponding table.

Spiegeleieren
oil on canvas -100x 80cm
Nuria Juncosa - 2003