Rで有名絵画を安全に買いたい

3Ͱ༗໊ֆըΛ҆શʹങ͍͍ͨ !TBMUDPPLZ 5PLZP3 1

୭ʁ 2 !TBMUDPPLZ • 3ྺɿ೥͙Β͍͔ͳ • ۈઌɿ࿡ຊ໦ʹ͋Δ*5ܥͷձࣾ • ࢓ࣄ಺༰ɿ3%తͳ෦ॺͰ  
ɹɹɹ3Λ࢖ͬͨσʔλ෼ੳ԰͞Μ   ػցֶशͷॲཧ࡞੒ • झຯɿ෰ϑΝογϣϯඒज़ؗ८Γ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 3 +BDLTPO1PMMPL     ந৅දݱओٛͷ୅දతͳΞϝϦΧਓըՈ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 4 υϩοϓϖΠϯςΟϯά

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 5 ʰ/P ʱ ºNN

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 6 ʰ/P ʱ ºNN ೥݄ ݱ୅ඒज़඼࠷ߴֹ ౰࣌ ԯສυϧ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 7 ཉ͍͠ʂ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 8 ͚Ͳɺِ෺΋ଟͦ͏ʜ

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   ϑϥΫλϧߏ଄͕͋Δ͜ͱ͕Θ͔Δ

ϑϥΫλϧߏ଄ 10 ਤܗͷҰ෦Λ֦େ͢Δͱɺશମͱ૬ࣅ͢Δܗ ࣗݾ૬ࣅੑ ͕ଘࡏ͢Δߏ଄ FYγΣϧϐϯεΩʔͷΪϟεέοτ

ϑϥΫλϧ࣍ݩ ༰ྔ࣍ݩϋυϧϑ࣍ݩ 11 w ͲΕ͚ͩࣗݾ૬ࣅੑ͕͋Δ͔Λࣔ͢ྔ w ֤ۭؒํ޲ʹ-ʹॖΊΔͱɺ΋ͱͷਤܗΛຒΊΔʹ͸/-%ݸ ͷࣗݾ૬ࣅਤܗ͕ඞཁͱ͍͏͜ͱΛදݱ   w
ʙͷؒΛͱΓɺʹ͍ۙ΄Ͳࣗݾ૬ؔੑ͕ڧ͍ w γΣϧϐϯεΩʔͷΪϟεέοτͷ࣍ݩ਺͸ w ղੳతʹ͸#PY$PVOUJOHΞϧΰϦζϜʹΑΓਪఆ

#PY$PVOUJOHΞϧΰϦζϜ 12 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̍ର৅ը૾ΛҰลͷ௕͕͞-ͷϒϩοΫʹ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 13 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̍ର৅ը૾ΛҰลͷ௕͕͞-ͷϒϩοΫʹ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 14 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̎ର৅͕өΓࠐΜͰ͍ΔϒϩοΫͷ਺/ - Λ਺͑Δ

#PY$PVOUJOHΞϧΰϦζϜ 15 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ϒϩοΫେ͖͞-Λখͯ͘͞͠ର৅ը૾Λ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 16 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ର৅͕өΓࠐΜͰ͍ΔϒϩοΫͷ਺/ - Λ਺͑Δ

#PY$PVOUJOHΞϧΰϦζϜ 17 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ େ͖͞-Λখ͘͞͠ͳ͕Βର৅͕өΔϒϩοΫΛΧ΢ϯτ͢Δ   ɹ͜ͱΛ܁Γฦ͢

#PY$PVOUJOHΞϧΰϦζϜ 18 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ϒϩοΫͷେ͖͞-ͱΧ΢ϯτ਺/ - ͷ྆ର਺άϥϑʹ͓͚Δ   ɹճؼ௚ઢͷ܏͖͕ϑϥΫλϧ࣍ݩʹͳΔ log N(L)
= D log(L) + K ʢ,ఆ਺ʣ MPH/ - MPH- ޯ഑%ʹ ϑϥΫλϧ࣍ݩ

19 w ͳͥ͜ΕͰϑϥΫλϧ࣍ݩΛਪఆ͢Δ͜ͱ͕Ͱ͖Δͷ͔   ఆ͔ٛΒͷมܗ log N(L) = log( a
L )D log N(L) = D log(L) + D log(a) #PY$PVOUJOHΞϧΰϦζϜ ʢBɿਖ਼ͷఆ਺ʣ

20 δϟΫιϯϙϩοΫͷ࡞඼ͷ৔߹ w -DNͰϑϥΫλϧ࣍ݩ͕มԽ w %% -Ҏ্ %- -ະຬ ʰ#MVF1PMFT/VNCFS
ʱ MPH - NN MPH / #PY$PVOUJOHΞϧΰϦζϜ

ϙϩοΫͷֆըͷಛ௃ 21 ʢ̍ʣ̎छͷϑϥΫλϧύλʔϯ͔Β੒Δ ʢ̎ʣ༷ʑͳεέʔϧʹ͓͍ͯϑϥΫλϧੑ͕ଘࡏ ʢ̏ʣϑϥΫλϧ࣍ݩ͸ର਺άϥϑͷޯ഑͔ΒٻΊΕΔ ʢ̐ʣ%-ʼ%% ʢ̑ʣۙࣅۂઢͷඪ४ภ͕ࠩখ͍͞ d ʢ̒ʣ֤৭ͷ૚Ͱ্هͷ̑ͭͷಛ௃Λຬͨ͢

3Ͱ#PY$PVOUJOH 22 7PY31BDLBHF

3Ͱ#PY$PVOUJOH 23 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ը૾ॲཧ

3Ͱ#PY$PVOUJOH 24 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ϑϥΫλϧ࣍ݩΛٻΊΔ

3Ͱ#PY$PVOUJOH 25 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ྆ର਺άϥϑͱճؼ௚ઢͷՄࢹԽ 0 2 4 6 8 -7
-6 -5 -4 -3 -2 log(1/res) log(N) Box Counting method : D=1.5747

؆୯ʹ·ͱΊ 26 w δϟΫιϯϙϩοΫͷֆըʹ͸ϑϥΫλϧߏ଄͕ଘࡏ͢Δ   w ϑϥΫλϧߏ଄ͷϑϥΫλϧ࣍ݩΛղੳతʹٻΊΔͨΊʹ ͸ɺ#PY$PVOUJOHΞϧΰϦζϜΛ༻͍Δ   w
3Ͱ͸7PY3QBDLBHFͷCPY@DPVOUJOHؔ਺Ͱ࣮ߦͰ͖Δ

&/% 27 &OKPZ

ࢀߟࢿྉ 28 •RʹΑΔը૾ॲཧɿimagerύοέʔδͷ࢖͍ํ  https://htsuda.net/archives/1985  •ϘοΫεΧ΢ϯτ๏ʹΑΔඐഀބͷϑϥΫλϧ࣍ݩ  https://shiga-u.repo.nii.ac.jp/?action=repository_uri&item_id=1751

Rで有名絵画を安全に買いたい

Rで有名絵画を安全に買いたい

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3Ͱ༗໊ֆըΛ҆શʹങ͍͍ͨ !TBMUDPPLZ 5PLZP3 1

୭ʁ 2 !TBMUDPPLZ • 3ྺɿ೥͙Β͍͔ͳ • ۈઌɿ࿡ຊ໦ʹ͋Δ*5ܥͷձࣾ • ࢓ࣄ಺༰ɿ3%తͳ෦ॺͰ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 3 +BDLTPO1PMMPL     ந৅දݱओٛͷ୅දతͳΞϝϦΧਓըՈ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 4 υϩοϓϖΠϯςΟϯά

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 5 ʰ/P ʱ ºNN

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 6 ʰ/P ʱ ºNN ೥݄ ݱ୅ඒज़඼࠷ߴֹ ౰࣌ ԯສυϧ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 7 ཉ͍͠ʂ

δϟΫιϯϙϩοΫΛ஌͍ͬͯ·͔͢ 8 ͚Ͳɺِ෺΋ଟͦ͏ʜ

ϙϩοΫͷֆըΛղੳͨ͠ݚڀ 9 • Fractal analysis of Pollock’s drip paintings.

ϑϥΫλϧߏ଄ 10 ਤܗͷҰ෦Λ֦େ͢Δͱɺશମͱ૬ࣅ͢Δܗ ࣗݾ૬ࣅੑ ͕ଘࡏ͢Δߏ଄ FYγΣϧϐϯεΩʔͷΪϟεέοτ

ϑϥΫλϧ࣍ݩ ༰ྔ࣍ݩϋυϧϑ࣍ݩ 11 w ͲΕ͚ͩࣗݾ૬ࣅੑ͕͋Δ͔Λࣔ͢ྔ w ֤ۭؒํ޲ʹ-ʹॖΊΔͱɺ΋ͱͷਤܗΛຒΊΔʹ͸/-%ݸ ͷࣗݾ૬ࣅਤܗ͕ඞཁͱ͍͏͜ͱΛදݱ   w

#PY$PVOUJOHΞϧΰϦζϜ 12 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̍ର৅ը૾ΛҰลͷ௕͕͞-ͷϒϩοΫʹ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 13 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̍ର৅ը૾ΛҰลͷ௕͕͞-ͷϒϩοΫʹ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 14 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ̎ର৅͕өΓࠐΜͰ͍ΔϒϩοΫͷ਺/ - Λ਺͑Δ

#PY$PVOUJOHΞϧΰϦζϜ 15 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ϒϩοΫେ͖͞-Λখͯ͘͞͠ର৅ը૾Λ෼͚Δ

#PY$PVOUJOHΞϧΰϦζϜ 16 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ର৅͕өΓࠐΜͰ͍ΔϒϩοΫͷ਺/ - Λ਺͑Δ

#PY$PVOUJOHΞϧΰϦζϜ 17 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ େ͖͞-Λখ͘͞͠ͳ͕Βର৅͕өΔϒϩοΫΛΧ΢ϯτ͢Δ   ɹ͜ͱΛ܁Γฦ͢

#PY$PVOUJOHΞϧΰϦζϜ 18 ϑϥΫλϧ࣍ݩΛٻΊΔྲྀΕ ϒϩοΫͷେ͖͞-ͱΧ΢ϯτ਺/ - ͷ྆ର਺άϥϑʹ͓͚Δ   ɹճؼ௚ઢͷ܏͖͕ϑϥΫλϧ࣍ݩʹͳΔ log N(L)

19 w ͳͥ͜ΕͰϑϥΫλϧ࣍ݩΛਪఆ͢Δ͜ͱ͕Ͱ͖Δͷ͔   ఆ͔ٛΒͷมܗ log N(L) = log( a

20 δϟΫιϯϙϩοΫͷ࡞඼ͷ৔߹ w -DNͰϑϥΫλϧ࣍ݩ͕มԽ w %% -Ҏ্ %- -ະຬ ʰ#MVF1PMFT/VNCFS

ϙϩοΫͷֆըͷಛ௃ 21 ʢ̍ʣ̎छͷϑϥΫλϧύλʔϯ͔Β੒Δ ʢ̎ʣ༷ʑͳεέʔϧʹ͓͍ͯϑϥΫλϧੑ͕ଘࡏ ʢ̏ʣϑϥΫλϧ࣍ݩ͸ର਺άϥϑͷޯ഑͔ΒٻΊΕΔ ʢ̐ʣ%-ʼ%% ʢ̑ʣۙࣅۂઢͷඪ४ภ͕ࠩখ͍͞ d ʢ̒ʣ֤৭ͷ૚Ͱ্هͷ̑ͭͷಛ௃Λຬͨ͢

3Ͱ#PY$PVOUJOH 22 7PY31BDLBHF

3Ͱ#PY$PVOUJOH 23 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ը૾ॲཧ

3Ͱ#PY$PVOUJOH 24 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ϑϥΫλϧ࣍ݩΛٻΊΔ

3Ͱ#PY$PVOUJOH 25 γΣϧϐϯεΩʔͷΪϟεέοτͷϑϥΫλϧ࣍ݩΛٻΊΔ ྆ର਺άϥϑͱճؼ௚ઢͷՄࢹԽ 0 2 4 6 8 -7

؆୯ʹ·ͱΊ 26 w δϟΫιϯϙϩοΫͷֆըʹ͸ϑϥΫλϧߏ଄͕ଘࡏ͢Δ   w ϑϥΫλϧߏ଄ͷϑϥΫλϧ࣍ݩΛղੳతʹٻΊΔͨΊʹ ͸ɺ#PY$PVOUJOHΞϧΰϦζϜΛ༻͍Δ   w

&/% 27 &OKPZ

ࢀߟࢿྉ 28 •RʹΑΔը૾ॲཧɿimagerύοέʔδͷ࢖͍ํ  https://htsuda.net/archives/1985  •ϘοΫεΧ΢ϯτ๏ʹΑΔඐഀބͷϑϥΫλϧ࣍ݩ  https://shiga-u.repo.nii.ac.jp/?action=repository_uri&item_id=1751