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Fractal dimension is an appropriate indicator to describe the complexity of a certain geometry, and box-counting analysis is proved to be an effective and appropriate method for fractal dimension estimation which is widely used. However, traditional box-counting methods based on images may not always accurate especially in small box scale due to the restriction of pixels. This paper aims to introduce a method based on generating fractal and determining boxes by rigid mathematical definition to eliminate the deviation of each box scale and to carry out more dependable results. Several samples of the simple and recursive fractal are analyzed to verify the accuracy of the box-counting method based on mathematical definition and interval in this paper. Keywords: Fractal, Fractal dimension, Box-counting method

Heart disease is a common human disease with high morbidity and mortality. Timely and effective prevention and treatment is an urgent clinical problem. The pathogenesis of heart disease is complex and diverse, involving hypertension, diabetes, atherosclerosis, drug toxicity, thrombosis, infection and other aspects. LL-37, an endogenous peptide, is well known for its antimicrobial properties. In recent years, LL-37 has been found to have a variety of biological functions, including its role in the regulation of atherosclerosis, thrombosis, inflammatory responses, and cardiac hypertrophy. Engineered LL-37-related peptides were developed and proved to regulate the development of disease, which revealed its potential clinical application. A comprehensive review and summary of LL-37 is presented to clarify its role in heart disease and to provide a reference and direction for future research.