PORTFOLIO
A space of variable curvature.
My existence as an artist includes a research for connection and integration of mathematical bases with a creative spirit that attempts to create and interpret every moment experienced daily.
This project aims to identify the link between real parallels in logical-mathematical sciences and art by analyzing spatial conceptions. I intend to demonstrate how geometry can be complementary to artistic representation in the genesis of abstract concepts and the concretization of the mental model of reality.
Non-Euclidean geometry. The essence of the unconscious.
The true object of my painting – the creation of mental symbols – is replaced by images that are representations of geometric reality and environmental reality.
Space is made up of dots or specks that define a line. In this case, however, the lines are understood as potential trajectories of a movement, and indifferently to whether these movements are realized or not. The lines define through themselves some points as places of potential encounters. In other words, the surfaces are presented here visually as images of movement, but also as an indication of potential mental images.
Therefore, my mathematical analysis and geometric projection are not ends in themselves, but rather constitute a particular approach to the vision of the world, corresponding to a method of representation of being an artist.
Exponential function
As a function of the real variable x, ex is always positive and increasing. The negative semi-axis of the x-axis is a horizontal symptom of the graph. The exponential function is of great importance in many areas of mathematics, such as trigonometry, the study of differential equations, the theory of Taylor developments, the study of integral transforms. In mathematics, the exponential function is the exponentiation with base the Euler number; the choice of this particular value is motivated by the fact that, in this way, the derivative of the exponential function is the exponential function itself.
Exponential function
The attention placed on the curvature of scientific space is a further precious interpretation in contemporary art. A mental curvature understood as a union of spiritual values. Characterized by the ability to move from mathematics, overcome it through the imaginative capacity, to then incorporate it into a new way of understanding it.
Logarithm function
One of the most important properties of logarithms is that the logarithm of the product of two numbers is the sum of the logarithms of the two numbers themselves.
Logarithm function
An interpretation of duality of the spatial conception is proposed here, where it is precisely the mental thought that tries to connect two contrastingly different spaces by applying logical knowledge to build a visual projection of reality.
Sine function
Sine function
By defining the sine as the angle, we obtain the sine function, a trigonometric function of fundamental importance in mathematical analysis. The sine is by definition half of a chord, that is, a segment that joins two points (called extremes) of a circumference.
The imaginary curvature expresses a concrete internal path where rebellion and intuition meet and merge in an act of creation, but it also expresses a concrete path that takes place in space and time where personal knowledge and feelings intertwine and knot to build an infinite dialogue.
The Taylor series
The Taylor series of a function at a point is the representation of the function as a series of terms calculated starting from the derivatives of the function itself at the point.
The Taylor series
But there is a path even broader than that of a straight line journey, and it is the internal path of me as an artist. The changing states of mind in the process of a given work, my immersion in the object to be represented, my spiritual growth, the transition to a new way are the most substantial changes that make up a synthesis of research and organization.
Non-analytic functions
Non-analytic functions
Not all infinitely differentiable functions are analytic. That is, there exist f(x) whose Taylor series converges, but which represents a drastically different function from f(x). For example, the function defined piecewise as f(x) := exp(−1/x²) for x ≠ 0 and f(0) := 0: all its derivatives at x = 0 are zero, so its series Taylor series is the null series and its radius of convergence is infinite, even if the function is very different from the null function.
Therefore, my mathematical analysis and geometric projection are not ends in themselves, but rather constitute a particular approach to the vision of the world, corresponding to a method of representation of being an artist.
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