Application of Sierpinski Gasket in Real-Life
The Sierpinski Gasket represents a fractal set that utilizes self-similarity in solving real-life problems. One of the issues that this fractal concept has solved is obtaining a wider bandwidth at resonance frequencies. Typically, the resonant frequency produces maximum oscillation on bodies, resulting in waves hitting rocks or other obstructions. In such cases, it is difficult for wider bandwidths to be captured by devices such as phones or other network-using systems (Galewski, 2019). Nevertheless, introducing fractal sets such as the Gasket has facilitated better reception in resonant frequency through their incorporation in fractal antennae.
The fractal antennae harness the aspects of self-similarity and space-filling to facilitate the reception of multiband waves in most devices. During the antennae construction, the patterns are built such that many congruent repetitions are attained to facilitate getting many waves while simultaneously maintaining miniaturization. These devices are then incorporated into mobile phones to promote better communication through the Internet or voice calls. One of the companies that have prowess in the construction of fractal antennae is Motorola which used to build phones that could process the transmission of electromagnetic waves from a wider range. Besides, the Gasket facilitates the broad reception of waves, and the fractal antennae reduce the number of receivers that would have been used (Galewski, 2019). This reduction is facilitated by the Sierpinski carpet, which can be laid in the phone to perform the functions of approximately 10 antennae. Generally, phones have applied fractal antennae to promote seamless network reception.
Along with easing communication, fractal antennae have been applied in wireless and spatial communication. In wireless communication systems, fractal antennae have been incorporated in WLAN and UMTS systems, allowing people to access networks without having physical wires. For instance, one can connect to a WLAN network offered by their organization’s router in the comfort of their office without having to connect the cable to their devices. Additionally, the Gasket has facilitated the construction of the RF MEMS probes and ANN, which can encode messages in electromagnetic waves and also decode and transform the waves into data during spatial communication (Galewski, 2019). Generally, the Gasket can be used to make fractal antennae that build WLAN and ANN systems for wireless and spatial communication.
Instances Where Recursion Can or Can Not Be Applied
One instance that warrants the application of recursion is when the work at hand is complex. In some cases, one may be tasked with complicated roles or activities, such as traversing through a family tree to identify a particular individual or the etiology of a given condition among relatives. In such a case, the recursive approach will be the best option, as it will analyze the data presented and produce the most viable solution without needing to understand the order of operations. Complex procedures are worth recursion compared to the loop method, as the latter requires an individual to understand the pattern before executing the action (Hamouda et al., 2018). For example, one may be required to learn the objects’ array before printing when the loop method is applied.
On the other hand, the recursive approach is disadvantageous in situations that require fast coding techniques, more space for an action to be executed, and unbreakable conditions. During coding, people prefer using quick and efficient methods; thus, the recursive approach is normally sidelined as it fails to meet the fast speed that most coders choose. Additionally, the recursive method consumes more space than the iterative approach; thus, coders with less storage cannot apply recursion in their practice (Hamouda et al., 2018). Lastly, recursion often breaks conditions once it starts running, which provides leeway to stack overflow. Other methods should be applied in such situations compared to the recursive criteria.
References
Galewski, M. (2019). On the application of monotonicity methods to the boundary value problems on the Sierpinski gasket. Numerical Functional Analysis and Optimization, 40(11), 1344-1354.
Hamouda, S., Edwards, S. H., Elmongui, H. G., Ernst, J. V., & Shaffer, C. A. (2018). RecurTutor: An interactive tutorial for learning recursion. ACM Transactions on Computing Education (TOCE), 19(1), 1-25.