A Systematic Review of Fractal Theory and its Application in Geography and Urban Planning

Fractal has been considered asan optimized structure of nature and an effective tool for depicting spatial complexity. Acity can be deemed as a fractal system with self-similarity, andare,therefore, ideal candidates for fractal analysis. Recent decadeshave witnessed great strides in research on fractal cities invarious aspects of urban forms and structuresas well asurban development dynamics. Considering the deep and wide-ranging applications of fractal theory in explaining local and spatial complexities, this study aimed atconducting a systematic review and content analysis of research conducted on fractal in order to pinpoint practical and theoretical frameworks they can provide to specialists in the fields of geography and urban planning. To this end, a systematic review was carried outin three general stages ofstudy selection, evaluation,and synthesisof findings. Resultsshowedthat developingand emergingconcepts in theoretical and experimental studies, which has soughtto explaintherolesandapplications of fractal theoryin research andsimulations of the builtenvironmentcouldbe classifiedin 10 areasofpsychology, architecture, urban design, urban formand structure, urban boundaryshape, land use, urban traffic, urban growth modeling, urban hierarchy,and benefits of fractals. Studies related to urban formand structure (N=37)accountedforthe largest share of studies. In addition, key methodsleading to the development of fractal studies in the existingliterature were use of fractal dimension and Hausdorffdimension (34%), boundarydimension (24%), and network or box-counting dimension (14%) followed bypower law (PL) distributions, power laws, andpower-scale law(7%).