## Convex walks in a concave garden

# 2022

# Convex walks in a concave garden, 2022

Cotton fabric colored with dyes derived from plant leaves.

This project is developed around the concept of the problem, as a set of conditions that occur both in a mathematical space and at the same time in a physical location.

*“The problem as a differential structure endowed with an intrinsic genetic power to generate sense”*. ^{1}

Leaves from different trees and plants were collected from the backyard of the Berg van Barmhartigheid building in Ghent, Belgium, during the autumn of 2022.

The features of each plant in the garden, and therefore those of the collected leaves, form a combined response to the problem of managing water resources, changes in the amount of daylight and temperature, quantity of chlorophyll, the attraction to birds, the protection from UV light, etc.

For instance, the trees detect less sunshine in the fall when the days begin to shorten. In response to stimulation, the plant sends signals instructing the leaves to change color and fall. The absence of chlorophyll makes it possible for the shine in their orange and yellow tones, while anthocyanin is responsible for the reddish color of tree leaves.

All the plants of the garden respond to their environment in a variety of ways, thus, we can think of the overall image of this yard as the union of the responses that each plant, tree, flower, and herb find to manage the changes of their milieu in this time period. We can view the garden as something that enables these issues to be localized,

*a problematic field, in which the solutions are organized.*

At the same time, a polyhedron can be constructed as the intersection of a number of half-spaces, each defined by a plane in three dimensions. These planes that divide the 3d space constitute also the faces of the bounded polyhedron.

The produced shape is defined as the solution set of a finite number of linear inequalities that are derived from these planes. In other words, the polyhedron is an expressed response to the simultaneous presence of these planes and the way they divide the same space.

This may not be that dissimilar from how we conceived our yard as a collection of solutions for the coexistence of plants with other living and non-living objects in the same space.