▁limited ▁by ▁integer ▁values . ▁This ▁is ▁possible ▁given ▁that ▁a ▁smaller ▁section ▁of ▁the ▁f ract al ▁res emb les ▁the ▁entire ty , ▁showing ▁the ▁same ▁statistical ▁properties ▁at ▁different ▁scales . ▁This ▁characteristic ▁is ▁term ed ▁scale ▁in var iance , ▁and ▁can ▁be ▁further ▁categor ized ▁as ▁self - similar ity ▁or ▁self - aff inity , ▁the ▁latter ▁scale d ▁an is otrop ically ▁( dep ending ▁on ▁the ▁direction ). ▁Whether ▁the ▁view ▁of ▁the ▁f ract al ▁is ▁expand ing ▁or ▁contract ing , ▁the ▁structure ▁remains ▁the ▁same ▁and ▁appears ▁equival ently ▁complex . ▁F ract al ▁analysis ▁uses ▁these ▁underlying ▁properties ▁to ▁help ▁in ▁the ▁understanding ▁and ▁character ization ▁of ▁complex ▁systems . ▁It ▁is ▁also ▁possible ▁to ▁expand ▁the ▁use ▁of ▁f ract als ▁to ▁the ▁lack ▁of ▁a ▁single ▁characteristic ▁time ▁scale , ▁or ▁pattern . ▁ ▁Further ▁information ▁on ▁the ▁Orig ins : ▁F ract al ▁Ge ometry ▁ ▁Types ▁of ▁f ract al ▁analysis ▁ ▁There ▁are ▁various ▁types ▁of ▁f ract al ▁analysis , ▁including ▁box ▁counting , ▁lac un ar ity ▁analysis , ▁mass ▁methods , ▁and ▁mult if ract al ▁analysis . ▁A ▁common ▁feature ▁of ▁all ▁types ▁of ▁f ract al ▁analysis ▁is ▁the ▁need ▁for ▁benchmark ▁patterns ▁against ▁which ▁to ▁assess ▁outputs . ▁These ▁can ▁be ▁acquired ▁with ▁various ▁types ▁of ▁f ract al ▁generating ▁software ▁capable ▁of ▁generating ▁benchmark ▁patterns ▁suitable ▁for ▁this ▁purpose , ▁which ▁generally ▁differ ▁from ▁software ▁designed ▁to ▁render ▁f