Chaotic

Engineering

Pure mathematics

CHAOS (operating system)

Discrete mathematics

Quaternion

Multivariable calculus

Control engineering

Computer security

Julia set

Dimension (graph theory)

Operating system

Set (abstract data type)

Computer science

Dentistry

The Imaginary

Fractal

Calculus (dental)

Psychology

Mathematics

Bijection

Fractal dimension

Psychotherapist

Attractor

Mathematical analysis

Artificial intelligence

Geometry

Universal set

Medicine

Programming language

Time-scale calculus

Fractional calculus

Space (punctuation)

Chaos Solitons & Fractals

Human being live in three-dimensional space; they can accurately visualize processes taking place in one, two and three dimensions. Although the set of bi-complex numbers and quaternion have attracted attention of many researchers in physics and related branches, they do not really represent processes taking place in the space where human being are located. We suggested a new set of complex number called "the Trinition". The new set is comprised between complex number with one imaginary part and complex number with three imaginary parts called quaternion/bi-complex numbers. We established a bijection between the new set and the three-dimensional space. We presented some important properties of the new set. We showed that all chaotic attractors in three dimension are simply three-dimensional mapping in the new set. Fewer examples of mapping in such set were presented. A new methodology that can be used to obtain more strange attractors are equally suggested. The methodology combines fractional chaotic models and some fractal mapping within the new set. Some illustrative figures are presented.

Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus