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Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

Golla et al. | Dec 14, 2020

Discovery of the Heart in Mathematics: Modeling the Chaotic Behaviors of Quantized Periods in the Mandelbrot Set

This study aimed to predict and explain chaotic behavior in the Mandelbrot Set, one of the world’s most popular models of fractals and exhibitors of Chaos Theory. The authors hypothesized that repeatedly iterating the Mandelbrot Set’s characteristic function would give rise to a more intricate layout of the fractal and elliptical models that predict and highlight “hotspots” of chaos through their overlaps. The positive and negative results from this study may provide a new perspective on fractals and their chaotic nature, helping to solve problems involving chaotic phenomena.

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Fractals: Exploring Mandelbrot Coordinates and qualitative characteristics of the corresponding Julia Set

Thomas et al. | Jul 07, 2022

Fractals: Exploring Mandelbrot Coordinates and qualitative characteristics of the corresponding Julia Set

Here based on an interest in fractals, the authors used a Julia Set Generator to consider a specific point on the Mandelbrot set with an associated coordinate. In this manner, they found that the complexity of the Mandelbrot and Julia Sets are governed by relatively simple rules, revealing that the intricate patterns of fractals can be defined by defined by simple rules and patterns.

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Impact of hog farming on water quality of aquatic environments in North Carolina

Kancharla et al. | Aug 08, 2023

Impact of hog farming on water quality of aquatic environments in North Carolina

This study collected samples from water bodies near hog farms and an aquatic environment not near a hog farm. It was hypothesized that water bodies near the hog farms would have lower water quality with higher turbidity, total dissolved solids (TDS), and pH than the water body not in proximity to a hog farm because of water contamination with hog waste. Results showed that the turbidity was 4–6 times higher, TDS was 1.5–2 times higher, and pH was 3 units higher in the 2 experimental locations compared to the control location. This study and its findings are important for understanding the impact of hog farming on the proximal water bodies.

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