As a relatively new and mathematics-related discipline, fractal has had a certain influence on the development of many aspects of today's society. At the same time, the science of fractal geometry to explore and study the practical use of fractal properties and fractal geometry is called a fractal theory. What's more, the emergence of fractal theory has promoted the development of various fields, provided new solutions and methods for some problems, provided a both logical and rigorous reference basis for some decisions, and also facilitated people's lives. By observing actual life and consulting some relevant literature, this article discusses the application of fractal theory in real life mainly from the aesthetics, health, and safety, respectively from three angles which are aesthetic art, medical and health, and highway traffic, such as pattern, numerical reference, material selection and so on, to understand the value of fractal theory in academic development and life application.

土地利用空间格局研究是土地利用/覆盖变化（LUCC）理论和实践的基础,对土地利用空间格局进行有效刻画有利于国土资源空间优化,提升土地利用规划和管理水平。由于土地利用空间格局的研究范畴尚不明晰,目前土地利用空间格局的研究对形状、斑块分布和结构等方面关注较少,缺乏对不同土地利用类型间相互关系的研究;同时,格局指标繁多且存在较大的相关性,如何建立指标与土地利用空间格局的对应关系值得进一步研究。本文在深刻理解土地利用空间格局内涵的基础上,将面积、形状和斑块分布总结为土地利用几何特征,将结构和多样性总结为土地利用类型特征,建立了土地利用空间格局刻画指标体系,利用模糊C均值聚类分析,明确了指标与空间格局间的对应关系。结果表明,中国土地利用几何特征可以划分为简单大斑块型、复杂大斑块型、复杂小斑块型、简单小斑块型和散布型五种,不同的几何特征反映了不同土地利用类型的面积、形状和斑块分布的特点,体现了区域土地利用类型的组合关系。2010年中国土地利用共存在61种不同的结构,但主要的结构类型仅有14种,结构特征具有明显的空间聚集性,体现了不同土地利用类型的空间分异性。中国土地利用多样性以3~5类为主,占比达66.69%,其特征总体上呈现“东北、东南高,西北低”的态势。该研究丰富了土地利用空间格局研究的理论体系,填补了中国土地利用整体空间格局刻画的空白。

系统揭示中国耕地景观细碎化的多尺度特征演进规律并就其未来发展趋势进行预测，对优化耕地资源利用与管理、促进农业适度规模经营等具有重要意义。本文以耕地景观细碎化的理论认知为基础，基于中国土地利用数据，集成泰尔指数、尺度方差及分解、马尔可夫链等数理统计和空间分析方法，按照国家、农业区、省域、市域、县域5级尺度，深入探讨1990—2020年中国耕地景观细碎化的多尺度特征演进规律与尺度嵌套效应，并据此预测其长期演变趋势。结果表明：① 中国耕地景观细碎化的格局特征具备明显的空间尺度差异，细碎化指数在县域以地势三级阶梯分界线成梯状分布，在市域依托“胡焕庸线”形成东低西高的“双核心—环核群—带状区”分异格局，在省域则呈现由东向西、自东北至西南逐级提高的同心圆圈层式结构。研究期内县域、市域、省域、农业区尺度差异对中国耕地细碎化总体差异的平均贡献分别为84.87%、14.64%、0.31%、0.18%，尺度越小越能反映耕地细碎化的空间异质性。② 1990—2020年中国耕地景观细碎化呈增强态势，但随时间推移增速减缓，并在2017年以后呈现出明显的减弱态势。其中，2000—2010年是耕地细碎化发展最为剧烈的时期，在不同尺度下均呈现细碎度增长幅度最大、覆盖范围最广、涉及维度最多等特点。③ 近30年中国耕地景观细碎化总体表现为“东增西减”，但不同尺度下耕地细碎化时空演变的趋势、强度、范围等存在较大差异。总体上，经济发达且农业资源禀赋优越的黄淮海平原、长江中下游平原中东部、四川盆地等地区是耕地细碎化增强的高值集聚区。④ 耕地景观细碎化的长期演变将遵循由低向高渐次递增的发展过程，低、较低等级细碎度县域将大幅减少，较高、高等级的县域将明显增加，同时，邻域背景对耕地细碎化的发展演化发挥重要作用。

Global land cover (LC) changes threaten sustainability and yet we lack a comprehensive understanding of the gains and losses of LC types, including the magnitudes, locations and timings of transitions. We used a novel, fine-resolution and temporally consistent satellite-derived dataset covering the entire Earth annually from 1992 to 2018 to quantify LC changes across a range of scales. At global and continental scales, the observed trajectories of change for most LC types were fairly smooth and consistent in direction through time. We show these observed trajectories in the context of error margins produced by extrapolating previously published accuracy metrics associated with the LC dataset. For many LC classes the observed changes were found to be within the error margins. However, an important exception was the increase in urban land, which was consistently larger than the error margins, and for which the LC transition was unidirectional. An advantage of analysing the global, fine spatial resolution LC time-series dataset is the ability to identify where and when LC changes have taken place on the Earth. We present LC change maps and trajectories that identify locations with high dynamism, and which pose significant sustainability challenges. We focused on forest loss and urban growth at the national scale, identifying the top 10 countries with the largest percentages of forest loss and urban growth globally. Crucially, we found that most of these 'worst-case' countries have stabilized their forest losses, although urban expansion was monotonic in all cases. These findings provide crucial information to support progress towards the UN's SDGs.