# :INFLECTIONS

INFLECTIONS is a real-time generative system that temporally rearranges video sequences based on mathematical equations. It explores the relationship between duration, simultaneity, and expectation.

The following clip is a short excerpt:

Technical concept

The technical concept of the work is based on the idea of a one-dimensional random walk: a mathematical representation of a journey along a linear path. The path contains several nodes or decision points. At each node along the path, the walker decides at random whether to go forward or backwards.

In this work, the “path” is the timeline of a movie clip. The program identifies a set of "inflection points" (or “decision points”) along this timeline. An inflection point is a moment that contains no motion, where movement comes to a standstill. It is thus a good point to change direction. Imagine now the computer program walking along a movie timeline. When it reaches one of those inflection points, it makes a yes-no decision, either to go forward or move back.

The following video explains the technical concept:

In this project, the walk is not random, because the program relies on some non-linear dynamical equation to make each decision. Inflections uses equations that exhibit chaotic behavior and for this reason can be used to simulate a random process.

The above clip was generated by means of the difference equation often known as the Logistic Map:

The program advances the movie forward or backward based on successive outputs of this equation.

For each decision point, the program uses this formula to generate a number. These numbers will always be in the interval between 0 and 1 (not inclusive). Each number drives the clip move forward or backward, based on this twofold rule:

1. If the number > 0.5, move forward to the next inflection point.

2. Otherwise, move back to the previous inflection point.

The behavior of the formula depends on the value of the parameter (the letter “r” in the formula above). When this value is 4.0 or slightly lower, the formula behaves in a way that "seems" random (pseudo-random). The succession of numbers follows no apparent logic. Its behavior in those cases is called "chaotic" because it looks random even though it is not.

The three images in the above video demo show how the same clip evolves with different values of r.

r = 3.8
r = 3.85
r = 4.0

01001000 01100101 01100011 01110100 01101111 01110010 00100000 01010010 01101111 01100100 01110010 01101001 01100111 01110101 01100101 01111010