Moving Parabola
Source: [Bra02]
The parabola is an important concept in abstract mathematics, but it is also a frequent phenomenon in the physical world, with many practical applications in engineering, physics, and other domains.
![](images/parabola.png)
A parabola
The base function for the dynamic problem is a parabolic equation of n dimensions:
![](images/parabolaFormula.png)
Changes in the environment are performed by shifting the parabola, where the size of the shift can control the severity of change. At least three models of change have been studied in the literature: linear, random and circular dynamics.
- Linear translation:
- Random dynamics:
- Circular dynamics:
![](images/linearTranslation.png)
![](images/randomDynamics.png)
![](images/circularDynamics.png)