Hyperbolic spiral

Hyperbolic spiral

Spiral Dynamics Algorithms

Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017

A hyperbolic spiral and an Archimedean spiral may be obtained from each other by inversion with respect to the pole O of the hyperbolic spiral. Using the representation of the hyperbolic spiral in polar coordinates, the curvature can be found by k=r2+2rθ2−rrθθ(r2+rθ2)3/2rθ=drdθ=−aθ2rθθ=d2rdθ2=2aθ3

A Developed Approach to Solve Economic and Emission Dispatch Problems Based on Moth-Flame Algorithm

View Article

Journal Information

Published in Electric Power Components and Systems, 2021

Abdel-rahem Hussien, Salah Kamel, Mohamed Ebeed, Juan Yu

Thus, enhancing the transfer orientation of moths can enhance the searching abilities of MFO. The modified MFO is characterized by logarithmic spiral movement of moths around the flames in the search space as given in (19) [12]. To clarify the idea of the hyperbolic spiral, it is worth mention the concept of Archimedean spiral which starts in the origin and makes a curve in the shape of spiral. Whereas hyperbolic spiral is the reverse of Archimedean spiral, where the origin is the end point in hyperbolic spiral starting from infinity (Figures 3 and 4).

Explore chapters and articles related to this topic

Spiral Dynamics Algorithms

A Developed Approach to Solve Economic and Emission Dispatch Problems Based on Moth-Flame Algorithm