# The Iterative Method by Leonardo Betti

Octavian C. on

Digital artist Leonardoworks, a.k.a Leonardo Betti believes math and physics could explain human life, perception, and “even the feelings we can not quantify, like love, that goes beyond time and space dimensions.” In a colorful algorithmic experiment, he delves into computational mathematics, using the iterative method, a way of generating a sequence of approximate solutions to a problem

Every shape, line or movement of The Iterative Method hasn’t been put together in a software suite but has been originated by an array of numbers (variables) set into formulas created by artist himself and that followed the paradigm of Quantic Physics. That is to say that Leonardo didn’t know the visual outcome of the artworks he was creating, just that if the math was correct they were going to appear as an orderly shape—the incredible beauty of the project lies both in the final result and in the creative process, which required an astonishing amount of skills and knowledge.

### The iterative method:

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method. An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In the problems of finding the root of an equation (or a solution of a system of equations), an iterative method uses an initial guess to generate successive approximations to a solution. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution. Iterative methods are often the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power.

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