A UHF band square Koch fractal slot antenna's design, production, and testing are described in [14]. With a length of 56.56 centimetres, the antenna is designed to fit inside the typical CubeSat faces, which are 10 cm by 10 cm. A schematic illustration of the suggested antenna design is shown in Fig. 3 [14], where it is positioned on the surface of a 1U CubeSat, which measures 10 cm by 10 cm. The antenna's diagonal length, which represents the antenna's overall length at each iteration, is 14.14 cm for the 0th iteration, 28.28 cm for the first iteration, and 56.56 cm for the second.

The antenna geometry consists of multiple iterations of koch curves, with each iteration increasing the total length of the antenna. The dimensions and placement of the antenna feed are determined based on parametric studies and simulations to achieve better impedance matching.

Fig. 4 [14] depicts a top view of the slot antenna, which allows for a clear visualization of the antenna's physical structure and layout

This antenna is designed for use in a CubeSat satellite and is part of a fractal slot antenna system. The top view shows the central part of the antenna, which measures 10 cm×10 cm, located on a Printed Circuit Board (PCB) laminate.

The details regarding the specific methodology or techniques used for this formation are not provided in the given context [14].

The antenna main characteristics' simulations are visualized in Fig. 6 and Fig. 7 [15], show the reflection coefficient, impedance bandwidth, antenna patterns, realized gain, and efficiency at different frequencies a. b.

Fig. 8 [15] displays the three-dimensional radiation pattern of an antenna, which provides information about how the antenna radiates electromagnetic energy in different directions at these specific frequencies.

A specialised fractal antenna, a Field Programmable Gate Array (FPGA), and Software-Defined Radio (SDR) are part of the BuhoSat's main payload [16] that is designed to detect synchrotron emission from electrons in the Van Allen belt. Scientists can learn important details about the characteristics of the ionised gas in the F region of the ionosphere and the Earth's atmosphere by examining the spectra recorded by this device. On another separate note, the main instrument of the BuhoSat is designed to capture electromagnetic radiation centered at 3.8 GHz [16]. It utilizes a fractal antenna based on the Sierpinski carpet (corresponding to Df, N = 3 and ε = 0.5), which allows it to capture synchrotron radiation emitted by spinning electrons about magnetic lines. A powerful FPGA and SDR are used to process the captured radiation, enabling the spectrum analysis in the frequency domain. This is illustrated by Fig. 9 [16].

The BuhoSat mission requirements provide specifications and verification criteria for various aspects of the satellite's design, such as protection of components, power supply, communication capabilities, imaging capabilities, data storage, and environmental requirements. The graphical representation serves as a visual aid to understand the overall design and functionality of BuhoSat.

Small and lightweight, CubeSats (known as LEO satellites) can be constructed with off-the-shelf parts and designed to operate in Low Earth Orbit (LEO). Compared to medium-sized satellites, they are less functional but can be developed more quickly and at a lower cost. CubeSats depend on the Telemetry, Tracking, and Communications (TTC) subsystem, and creating antennas for them is difficult because of their limited size, weight, and power [17]. Fig. 10 [17] lists the three typical CubeSat types 1U, 2U, and 3U and their corresponding sizes.

a. b. c.

To address this issue, a deployable microstrip patch antenna with a fractal architecture for 1U CubeSats was created [17]. By utilising the Koch snowflake fractal structure (corresponding to Df, N = 4 and ε = ). Its omnidirectional layout does, however, result in less gain. The proposed antenna (see Fig. 11 [17]) achieves a compact size, high gain, minimal reflection coefficient, big bandwidth, and good impedance matching.

In [18], fractal pedagogy's theoretical and methodological foundations, as well as its principles and features, were discussed. The research aimed [18] to identify the components of personal and professional self-development for teachers, including motivation, design, practical activities, reflection, and emotional volition. So, in principle, [18] provided a new perspective on the problem of teacher self-development and suggests that fractal methodology can serve as a basis for further psychological and pedagogical research in this area. The principle of fractality [18] applies to various social processes, allowing us to understand different aspects of life from a fractal perspective. Examples of fractal organization can be seen in socio-cultural systems such as language, music, architecture, and patterns, highlighting the multifaceted nature of these phenomena. The term "conceptual fractal" [18] describes the self-multiplying nature of socio-cultural practices and their organization at different levels and scales, ultimately contributing to the overall structure of the socio-cultural world.

More fundamentally, Fractals [18] are not a new concept in technical sciences and are used as a basis for various scientific disciplines. Fractal methodology involves studying social systems at different levels, recognizing cyclical trends and the legitimacy of events, and creating socio-political and other fractal models [18]. In the context of personal and professional self-development in education, fractal methodology is employed to understand the process from a fractal theory perspective, with an integrated-ecological methodological approach being the leading approach in studying the organization of this process [18]. The importance of highly qualified specialists in ongoing reforms and developing a mature training system in Uzbekistan [19] was highlighted. Fractals, complex objects based on simple laws, have similarities with natural phenomena and can be used to predict various factors, such as the growth rate of plant root systems and the mass of straw dependent on branch length [19].

According to [19], it is recommended to incorporate fine arts and teaching practices that consider the specificities of fine and applied arts to enhance students creative abilities. By utilizing facts in applied art compositions, color palettes, and graphics, students can develop their observation skills, stimulate their imagination, and recognize the fractal nature of objects [19]. Fractals, complex structures governed by simple laws, share similarities with various natural phenomena, ranging from crystals and ecosystems to biological objects, highlighting the interconnectedness of art and nature [19].

A novel fractal approach to teaching physical and mathematical disciplines is presented to promote independent and original computer modelling of natural processes [20]. Encapsulation, inheritance, and polymorphism, three core tenets of object-oriented programming, have demonstrated their power in influencing how various academic fields perceive information architecture's physical and mathematical components [20]. This method can potentially be applied to other areas of physics, as shown [20]. The study of the Geometric Optics and Wave Optics portions of physics is used to illustrate how the generated iterations of the fractal structure are displayed [20], including a new iteration results in a high-quality and in-depth perception of new information, demonstrating how each iteration is characterised by synergy [20].

A fractal is an information-branched structure whose spatial dimension is characterised by a fractional number in the context of applying physical and mathematical education [20]. When creating complex structures, this property of fractality ensures the accuracy and completeness of information flows. However, minimal energy dissipation and energy-informational self-similarity are used to achieve complexity [20]. This demonstrates the effectiveness and appropriateness of their implementation in teaching science pedagogical subjects, which are currently underdeveloped and underargued. Geometric, algebraic, and stochastic fractal characteristics (Fig. 12, [20]) can be seen as characteristics of how the instructional process works.

A complicated application of aspects of geometric, algebraic, and stochastic fractals was used to build iterations of the fractal structure as it relates to the study of the physics sections Geometric Optics and Wave Optics [20]. In Figs. 14-17, the concepts and growth of the fractal structure's branches are depicted. It should be emphasised that the encapsulation, inheritance, and polymorphism concepts used in computer modelling are also founded on these concepts. It is object-oriented modelling, in other words.

physical education data [20].

optics" and "wave optics" [20].