scholarly journals Penerapan Modifikasi Fraktal Segitiga Sierpinski pada Ragam Hias Geometris Tumpal

2022 ◽  
Vol 9 (2) ◽  
pp. 165-174
Author(s):  
Miftahur Roi'fah
Keyword(s):  
Isosceles Triangle ◽  
Self Similarity ◽  
Sierpinski Triangle ◽  
Basic Frame

Abstract 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

AROUND THE SIERPINSKI TRIANGLE. THE CHAOS GAME AND THE SCRATCH PROGRAMMING

2020 ◽  
pp. 20-26
Author(s):  
L. V. Denisova ◽  
V. O. Dzhenzher
Keyword(s):  
Programming Language ◽  
The Self ◽  
Self Similarity ◽  
Transparent Films ◽  
Fractal Sets ◽  
Sierpinski Triangle ◽  
Random Events ◽  
Cutting Out ◽  
Chaos Game ◽  
Small Rotation

The article discusses the experience of studying Sierpinski geometric fractals in circle classes in mathematics and informatics with students of grades 4–6. A versatile approach to the construction of fractal objects is used: a method of cutting out of paper, Chaos Game on transparent films and implementing the studied algorithm in the Scratch programming language. At the same time, some issues related to the occurrence of random events are discussed with the children. After the fractal is obtained on a computer, the research phase of the constructed model follows. In the computer Chaos Game: (1) a small rotation by a specified number of degrees is sequentially added before setting the next point; (2) a turn in front of individual fractal vertices; (3) compression of a fractal to individual vertices. Conclusions are drawn about the self-similarity of the resulting objects. The proposed method allows us to study some properties of fractal sets, by involving visualization, intuition and computer modeling.

Variation Of Rotation In Chaos Game By Modifying The Rules

2020 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Rana Arij Afifah ◽  
Kosala Dwidja Purnomo ◽  
Firdaus Ubaidillah ◽  
Ismail Husein
Keyword(s):  
Reference Point ◽  
Reference Points ◽  
Core Concept ◽  
Self Similarity ◽  
Center Of Rotation ◽  
Sierpinski Triangle ◽  
The Core ◽  
Chaos Game ◽  
Visual Results

<span>The core concept of fractals is the process of rearranging identical components that have a large amount of self-similarity. One example of fractals is the Sierpinski trianglecan be generated using the chaos game method. This method is a form of play in drawing points on triangles that have certain rules and are repeated iteratively. This research will modify the rules of chaos game triangle with the addition of various rotationswith the center of rotation at one, two, three, four, and five reference points. The visual results obtained are in the form of fractals because they have self-similarity properties and a collection of new points formed experiences rotation with the center of rotation based on the selected reference point with the direction of rotation based on the rules. The visual results of the rotation </span><span>θ</span><span> angle are visually symmetrical about the axis-y with the visual results of the rotation 360</span><span>⁰</span><span>-</span><span>θ</span><span>  angle at one, three, four, and five reference points as the center of rotation. At two reference points as the center of rotation it is obtained that there are two parts that are visually symmetrical about a certain line. Visual results of rotation 360</span><span>⁰</span><span> angles at one, two, three reference points as the center of rotation have a shape similar to the Sierpinski triangle. Whereas at four and five points of reference as the center of rotation has a shape similar to the Sierpinski triangle.</span>

Beckett's Broken Circle: A Literary Fractal

2020 ◽  
Vol 29 (2) ◽  
pp. 196-215
Author(s):  
Luke Connolly
Keyword(s):  
Dynamic Chaos ◽  
Geometric Form ◽  
Self Similarity ◽  
Collision Point ◽  
Stable Order ◽  
Structural Principle ◽  
Recent Interest ◽  
Viable Solution ◽  
Specific Shape

This essay proposes that the picture of a broken circle encountered by Watt during the second part of his tale marks a crucial collision point between Beckett's literary and mathematical interests and triggers a process of fractal scaling self-similarity. Building on recent interest concerning the role of the mathematics and mathematical forms found in Beckett's work, I argue that the broken circle depicted in the picture from Watt is a geometric form which (re)appears within at least three interlocking scales throughout Beckett's novel-length prose: (i) its moment of arrival in the picture from Watt, (ii) a macroscopic reinscription in the names of the protagonists populating the five novels spanning Watt through to The Unnamable and (iii) buried within the narratological depths of How It Is. As a structural principle, the interminable irregularity of fractals offered Beckett a viable solution for what he considered the defining task of the modern artist: ‘to find a form to accommodate the mess’. Moreover, the specific shape selected for his fractal is shown to contain within its geometry one of Beckett's most universal and pressing concerns: the inevitable insufficiency of language. Therefore, although this essay restricts itself to examining Beckett's novel-length prose, the idea of a broken circle fractal promises to provide a valuable heuristic through which to reassess the author's other generic avenues. Fractals thus offer a means through which one can bind together the length and breadth of Beckett's oeuvre without ever reducing dynamic chaos to stable order.

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