Penerapan Modifikasi Fraktal Segitiga Sierpinski pada Ragam Hias Geometris Tumpal

Sierpinski’s triangular fractal is a linear fractal that has self-similarity, which is identical until infinite iterations. This research aims to develop the Tumpal geometric ornaments with the implementation of modified Sierpinski’s triangular fractal. There are three algorithms that will be used. First, an algorithm to modify the Sierpinski triangle. The isosceles triangle is divided into nine congruent triangles. Then randomly selected several triangles to be left blank. Do the same way to the triangle that still exists until some iteration. Second, modeling the base frames. Third, fill the basic frame from the second algorithm with the modified Sierpinski's triangular fractal from the first algorithm into a motif. The results are various Tumpal geometric motifs with the implementation of modified Sierpinski’s triangular fractal. Keywords: linear fractal, Sierpinski’s triangular fractal, ornament, Tumpal geometric Abstrak Fraktal segitiga Sierpinski merupakan fraktal linier yang memiliki sifat self-similarity, yaitu identik sampai pada iterasi tak terhingga. Penelitian ini bertujuan untuk mengembangkan ragam hias geometris Tumpal dengan penerapan modifikasi fraktal segitiga Sierpinski. Ada tiga algoritma yang akan digunakan. Pertama, algoritma yang bertujuan untuk memodifikasi segitiga Sierpinski. Data awal berupa segitiga samakaki yang dibagi menjadi sembilan segitiga kongruen. Kemudian dipilih secara acak beberapa segitiga yang akan dikosongkan. Pada segitiga yang masih berisi dilakukan hal yang sama Kedua, modelisasi bingkai dasar. Ketiga, mengisi bingkai dasar hasil algoritma kedua dengan modifikasi segitiga Sierpinski hasil algoritma pertama sehingga menjadi sebuah motif. Hasil penelitian yang diperoleh adalah beragam motif geometris Tumpal dengan penerapan modifikasi segitiga Sierpinski. Kata Kunci: fraktal linier, segitiga Sierpinski, ragam hias, geometris Tumpal

The Interplay between Individual and Collective Activity: an Analysis of Classroom Discussions about the Sierpinski Triangle

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area and perimeter of the Sierpinski triangle, a unique mathematical object with zero area and infinite perimeter. As participants conceptualize and communicate about the Sierpinski problem, they unwittingly generate a linguistic register of action word forms (e.g., fencing, zooming) and object word forms (e.g., area, infinity) to serve Sierpinski-linked mathematical reasoning functions, a register that we document in the first analytic section of the article. In the second analytic section, we report a developmental analysis of microgenetic, ontogenetic, and sociogenetic shifts in the word forms constitutive of the register and their varied functions in participants’ activities. In the third analytic section, we provide a cultural analysis of the classroom’s collective practices, practices that enable and constrain participants’ constructions of form-function relations constituting the register. We examine the ways in which participants work to establish a common ground of talk in their communicative exchanges, exchanges supported by classroom norms for public displays of reasoning and active listening to one another’s ideas. We show that it is as participants work to establish a common ground that the register emerges and is reproduced and altered. We conclude by pointing to ways that the analytic framework can be extended to illuminate learning processes in other classroom settings.

Embroidered Βow-Tie Wearable Antenna for the 868 and 915 MHz ISM Bands

A textile, embroidered antenna, based on the fractal shape of the Sierpinski triangle, is designed in this paper for operation in the European free Industrial Scientific and Medical (ISM) 863–870 MHz band, as well as in the 902–928 MHz band designated for ISM applications in North and South America. Several prototypes have been fabricated by employing different stitch patterns and thread materials. The effect of the fabrication parameters on the performance of the proposed antenna is investigated through measurements and simulations, with the results being in good agreement. The antenna exhibits attractive characteristics such as wide bandwidth, relatively stable radiation patterns, as well as robustness in washing. Several tests reveal that convex and concave bent conditions do not affect the coverage of the aforementioned ISM bands, despite the shift of the resonant frequency in some cases. Moreover, the SAR values resulting from simulations are below the corresponding thresholds suggested by international guidelines.

Introdução à Geometria Fractal no Ensino Médio Técnico: Uma Abordagem com Programação Python

This work is inserted in the context of technical high school andit aimed to analyze the integration between the branches of FractalGeometry, Analytical Geometry and Computer Programming.For this purpose, we carried out a bibliographic search about whatcharacterizes and distinguishes Fractal Geometry from EuclideanGeometry, we also seek in our readings to list the most famousfractals. Then, we developed (in python language) several fractalgeneration programs. It was possible to work with amazing andeasily programmable fractal shapes, such as the Cantor Set, theHilbert Curve and Sierpinski Triangle. We also built two new familiesof fractal shapes from a generalization of the Koch Curve. Weconclude that programming fractals in the context of technical highschool is productive and challenging, as it requires many changesin the representations of fractal patterns.

Research of antenna complexes using chiral metamaterials and fractal geometry of radiators for MIMO systems

This article is devoted to the study of the possibilities of increasing spectral efficiency in MIMO systems by using antennas with substrates of biisotropic and bianisotropic chiral metamaterials and various types of fractal emitters, in particular, fractal structures in the form of a Sierpinski triangle, Koch and Gilbert curves, as well as a dipole triangular antenna of complex configuration FRM. The spectral efficiency was calculated by using one of the variations of the Shannon formula, which includes a complete matrix of Z-parameters. In turn, this matrix was determined using the software package of electrodynamic modeling. It is shown that the use of such antennas with the fractal geometry of the emitters located on chiral substrates reduces the mutual influence between the emitters, and, in turn, increases the spectral efficiency in several frequency ranges compared to traditional solutions.