TokyoR #101 LT
3Ͱ༗໊ֆըΛ҆શʹങ͍͍ͨ!TBMUDPPLZ5PLZP31
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୭ʁ 2!TBMUDPPLZ• 3ྺɿ͙Β͍͔ͳ• ۈઌɿຊʹ͋Δ*5ܥͷձࣾ• ࣄ༰ɿ3%తͳ෦ॺͰ ɹɹɹ3Λͬͨσʔλੳ͞Μ ػցֶशͷॲཧ࡞• झຯɿϑΝογϣϯඒज़ؗ८Γ
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 3+BDLTPO1PMMPL நදݱओٛͷදతͳΞϝϦΧਓըՈ
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 4υϩοϓϖΠϯςΟϯά
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 5ʰ/P ʱºNN
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 6ʰ/P ʱºNN݄ݱඒज़࠷ߴֹ ࣌ԯສυϧ
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 7ཉ͍͠ʂ
δϟΫιϯϙϩοΫΛ͍ͬͯ·͔͢ 8͚Ͳɺِଟͦ͏ʜ
ϙϩοΫͷֆըΛղੳͨ͠ݚڀ 9• Fractal analysis of Pollock’s drip paintings. (R.P.Taylor, et al , 1999) • On multifractal structure in non-representational art.(J.R.Nureika, et al , 2005) ˠϙϩοΫͷυϩοϓϖΠϯςΟϯάʹ ϑϥΫλϧߏ͕͋Δ͜ͱ͕Θ͔Δ
ϑϥΫλϧߏ 10ਤܗͷҰ෦Λ֦େ͢Δͱɺશମͱ૬ࣅ͢Δܗ ࣗݾ૬ࣅੑ͕ଘࡏ͢ΔߏFYγΣϧϐϯεΩʔͷΪϟεέοτ
ϑϥΫλϧ࣍ݩ ༰ྔ࣍ݩϋυϧϑ࣍ݩ 11w ͲΕ͚ͩࣗݾ૬ࣅੑ͕͋Δ͔Λࣔ͢ྔw ֤ۭؒํʹ-ʹॖΊΔͱɺͱͷਤܗΛຒΊΔʹ/-%ݸͷࣗݾ૬ࣅਤܗ͕ඞཁͱ͍͏͜ͱΛදݱ w ʙͷؒΛͱΓɺʹ͍ۙ΄Ͳࣗݾ૬ؔੑ͕ڧ͍w γΣϧϐϯεΩʔͷΪϟεέοτͷ࣍ݩw ղੳతʹ#PY$PVOUJOHΞϧΰϦζϜʹΑΓਪఆ
#PY$PVOUJOHΞϧΰϦζϜ 12ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ̍ରը૾ΛҰลͷ͕͞-ͷϒϩοΫʹ͚Δ
#PY$PVOUJOHΞϧΰϦζϜ 13ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ̍ରը૾ΛҰลͷ͕͞-ͷϒϩοΫʹ͚Δ
#PY$PVOUJOHΞϧΰϦζϜ 14ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ̎ର͕өΓࠐΜͰ͍ΔϒϩοΫͷ/ -Λ͑Δ
#PY$PVOUJOHΞϧΰϦζϜ 15ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕϒϩοΫେ͖͞-Λখͯ͘͞͠ରը૾Λ͚Δ
#PY$PVOUJOHΞϧΰϦζϜ 16ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕର͕өΓࠐΜͰ͍ΔϒϩοΫͷ/ -Λ͑Δ
#PY$PVOUJOHΞϧΰϦζϜ 17ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕେ͖͞-Λখ͘͞͠ͳ͕Βର͕өΔϒϩοΫΛΧϯτ͢Δ ɹ͜ͱΛ܁Γฦ͢
#PY$PVOUJOHΞϧΰϦζϜ 18ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕϒϩοΫͷେ͖͞-ͱΧϯτ/ -ͷ྆ରάϥϑʹ͓͚Δ ɹճؼઢͷ͖͕ϑϥΫλϧ࣍ݩʹͳΔlog N(L) = D log(L) + K ʢ,ఆʣMPH/ -MPH-ޯ%ʹϑϥΫλϧ࣍ݩ
19w ͳͥ͜ΕͰϑϥΫλϧ࣍ݩΛਪఆ͢Δ͜ͱ͕Ͱ͖Δͷ͔ ఆ͔ٛΒͷมܗlog N(L) = log(aL)Dlog N(L) = D log(L) + D log(a)#PY$PVOUJOHΞϧΰϦζϜʢBɿਖ਼ͷఆʣ
20δϟΫιϯϙϩοΫͷ࡞ͷ߹w -DNͰϑϥΫλϧ࣍ݩ͕มԽw %% -Ҏ্%- -ະຬʰ#MVF1PMFT/VNCFS ʱMPH -NNMPH /#PY$PVOUJOHΞϧΰϦζϜ
ϙϩοΫͷֆըͷಛ 21ʢ̍ʣ̎छͷϑϥΫλϧύλʔϯ͔ΒΔʢ̎ʣ༷ʑͳεέʔϧʹ͓͍ͯϑϥΫλϧੑ͕ଘࡏʢ̏ʣϑϥΫλϧ࣍ݩରάϥϑͷޯ͔ΒٻΊΕΔʢ̐ʣ%-ʼ%%ʢ̑ʣۙࣅۂઢͷඪ४ภ͕ࠩখ͍͞ dʢ̒ʣ֤৭ͷͰ্هͷ̑ͭͷಛΛຬͨ͢
3Ͱ#PY$PVOUJOH 227PY31BDLBHF
3Ͱ#PY$PVOUJOH 23γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔը૾ॲཧ
3Ͱ#PY$PVOUJOH 24γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔϑϥΫλϧ࣍ݩΛٻΊΔ
3Ͱ#PY$PVOUJOH 25γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ྆ରάϥϑͱճؼઢͷՄࢹԽ02468-7 -6 -5 -4 -3 -2log(1/res)log(N)Box Counting method : D=1.5747
؆୯ʹ·ͱΊ 26w δϟΫιϯϙϩοΫͷֆըʹϑϥΫλϧߏ͕ଘࡏ͢Δ w ϑϥΫλϧߏͷϑϥΫλϧ࣍ݩΛղੳతʹٻΊΔͨΊʹɺ#PY$PVOUJOHΞϧΰϦζϜΛ༻͍Δ w 3Ͱ7PY3QBDLBHFͷCPY@DPVOUJOHؔͰ࣮ߦͰ͖Δ
&/% 27&OKPZ
ࢀߟࢿྉ 28•RʹΑΔը૾ॲཧɿimagerύοέʔδͷ͍ํ https://htsuda.net/archives/1985 •ϘοΫεΧϯτ๏ʹΑΔඐഀބͷϑϥΫλϧ࣍ݩ https://shiga-u.repo.nii.ac.jp/?action=repository_uri&item_id=1751