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&RODERUDWRU\ ࡛ᙧࡢ⛉Ꮫࢆᴦࡋࡶ࠺̽ ➨  ᅇ ࢯ࣮ࢩࣕࣝࢹ࢕ࢫࢱࣥࢫࢆ⪃࠼ࡿ㸸%R[ ࡬ࡢࣛࣥࢲ࣒ࣃࢵ࢟ࣥࢢ ̽ᖹ⏣ 㝯ᖾ ····································································· ࠙఍࿌࡞࡝ࠚ
఍࿌···································································································· ཎ✏ເ㞟 ···························································································· ࿨ช‫ܙ‬͹Ռָճࢿ ୊ 35 ‫ ת‬୊ 2 ߺඉҲ༹͵‫ࢋܯ‬ब‫غ‬Ν࣍ͯඉಋ‫غ‬෾ࢆεϝϣϪʖν͗ਫ਼੔ͤΖ࣎‫ؔۯ‬ϏνʖϱࢃԮ‫ٳ‬य़ 1ː ) ɾᤜ౨ਫ਼ 2)1) ਈ಺ઔ‫ݟ‬ઔ࡜ࢤ߀ۢԾฑؔ 214-1
2)ஞഀ୉ָ୉ָӅεητϞ৚ๅ޽ָ‫ڂݜ‬Ռ*akoamay@gmail.com

6SDWLR-7HPSRUDO3DWWHUQV*HQHUDWHGE\DQ$V\QFKURQRXV'LVWULEXWHG6LPXODWRUZLWK1RQ-XQLIRUP&DOFXODWLRQ3HULRGVHisatoshi Yamaoka 1) , Cai Dongsheng 2)
1) Shimohirama Saiwai-ku, Kawasaki-shi, Kanagawa-ken
2) Graduate School of Systems and Information Engineering,
University of Tsukuba(2020 ೧ 9 ݆ 1 ೖण෉ɾ2020 ೧ 10 ݆ 15 ೖणཀྵ)Abstract: A spatiotemporal patterns generated by the simulator with spatially non -uniform
calculation period are observed. Regarding to the wave equation, simulation results showthat the spatio-temporal patterns of solutions obtained by non-uniform calculation periods
varies. Their qualitative properties can be roughly classified whether the wave sources arelocated in a region where the calculation period is slow or not. In the reaction -diffusion
equation, the difference in calculation period does not make a qualit ative difference in thespatial pattern. However, from the shape of the generated spatial pattern, it was possible toroughly see where the region with a slow calculation period exists.
Keywords: Asynchronous Distributed Simulator, Spatio-Temporal Patterns, Wave equation,
Reaction-Diffusion equation

1. ͺͣΌͶ
1.1. ‫ڂݜ‬͹ഐ‫ܢ‬߁Ү͵‫ؔۯ‬Νଲেͳͪ͢εϝϣϪʖεϥϱ͹ͪΌͶͺɾ‫ؔۯ‬Ν෵਼͹྘ҮͶ෾ׄ͢ɾ‫ݺ‬พ͹‫ؽࢋܯ‬ͶׄΕ౲ͱͪ৏Ͳɾด྽෾ࢆͲ‫ࢋܯ‬ΝࣰߨͤΖෝ՛෾ࢆ๏༙ࣞ͗ްͲ͍Ζ [1]ɿ͞͹Γ͑͵྘Ү෾ׄघ๑Ͷ΍ͳͰ͚୉‫و‬ໝ෾ࢆεϝϣϪʖν͹ߑ૟Νਦ 1 Ͷࣖͤɿt 89 tਦ 1ʁඉಋ‫غ‬෾ࢆεϝϣϪʖν͹ߑ੔͞͹෾ࢆεϝϣϪʖνͺɾଡ਼͹‫ࢢ֪͗ؽࢋܯ‬য়ͶϋρφϭʖέͲ݃߻ͪ͢ߑ੔ΝͳΕ ɿεϝϣϪʖεϥϱ‫ؔۯ‬Ν֪ࢢয়Ͷۢ઀ͮͱͨΗͩΗ͹‫ؽࢋܯ‬ͶׄΕ౲ͱΖ ɿ֦‫ؽࢋܯ‬ͺ‫ۯ‬ؔΝ཯ࢆԿ֪ͪ͢ࢢͳ͢ͱฯ࣍͠ΗɾͨΗΔ͹֪ࢢͶଲ͢ͱɾιϩΨʖφϜφϱΏɾยඏ෾๏ఖࣞΝ཯ࢆԿ͢ͱಚͪયҢ‫و‬ଉΝࡠ༽ͦ͠Ζɿ͍Ζ࣎ࠃ‫ݐ‬Ͷ͕͜ΖεϝϣϪʖεϥϱଲে͹ ‫ ܧ‬Ν ‫ݑ‬௧ ͳ͢ ɾͨ ͞ Ͷ ࡠ༽ ͠ ͦΖ ય Ң‫ و‬ଉ Ν ݂ͳͤ Ζ ͳɾ 1 յ ͹ ‫ ࢋܯ‬ητ ρ ϕͲ ‫ݑ‬௧ାଵ ൌ݂ሺ‫ݑ‬௧ ሻΝ‫ٽ‬Όɾ͞͹‫ࢋܯ‬ητρϕΝͨΗͩΗ͹‫܃͗ؽࢋܯ‬Εศͤ͞ͳͲ ɾ‫ؔۯ‬͹࣎ؔ൅ఴΝεϝϣϪʖεϥϱͤΖɿΉͪɾۢ෾ͪ͜͢‫ؔۯ‬͹‫ڧ‬ֆͶҒ஖ͤΖ֪ࢢ͹‫ࢋܯ‬͹ͪΌͶච གྷ͵‫ڧ‬ֆυʖνΝɾۛંͤΖ‫ࢋܯͳؽࢋܯ‬ητρϕ͹ౕͶ ϋρφϭʖέΝղ͢ͱૻण৶͢߻
͑ʤਦ 2ʥɿ

ਦ 2ʁϋρφϭʖέΝղͪ͢྘Ү‫ڧ‬ֆυʖν͹ૻण৶

͑ͤ͞Ζ͞ͳͲɾ‫ؽࢋܯ‬Νଁ͢ɾखΕѽ͑‫ؔۯ‬͹߁͠Ν֨୉͢ͱ͏͚͞ͳ͗Ͳ͘Ζɿ͖͢͢ɾ͞͹Γ͑͵෾ࢆεϝϣϪʖνͲͺɾ੓೵Ώෝ՛য়‫ڱ‬ͶΓΖҩ͏͖Δɾ‫ࢋܯ‬ητρϕͶ
གྷͤΖ࣎ؔ͗‫ݺ‬ʓ͹‫ͳ͟ؽࢋܯ‬Ͷҡ͵Ζɿͨ͹ͪΌɾ‫͵ືݭ‬εϝϣϪʖεϥϱΝߨ͑ͪΌt 90 tͶͺ‫ؽࢋܯ‬ಋ࢞͹‫ߨࣰࢋܯ‬ν΢ϝϱή͹ಋ‫॑͗غ‬གྷͳ͵Ζɿ ಋ‫غ‬ΝߨΚ͵͏৖߻ɾ֦‫ࢋܯ‬‫༙ݽ͗ؽ‬͹ब‫Ͳغ‬ඉಋ‫غ‬Ͷ‫ࢋܯ‬ητρϕΝ‫܃‬Εศͤ͞ͳͶ͵Εɾ‫ؔۯ‬৏͹৖ॶͶΓͮͱ࣎ؔ͹਒΋ଐౕ͗ҡ͵Ζ͞ͳͶ͵Ζɿಋ‫غ‬Νߨ͑ͪΌͶͺɾ‫ࢋܯ‬ητρϕࣰߨ͹ͪ;ͶɾۛંͤΖ౨੤ೈ๼ 4 ୈ͹‫͖ؽࢋܯ‬Δસͱ͖Δ‫ڧ‬ֆ֪ࢢυʖν͗ૻ৶͠Ηͱ͚ΖΉͲଶ‫ͤؽ‬Ζචགྷ͍͗Εɾ͞Η͗‫ࢋܯ‬ஙԈΝӀًͤ͘͞‫ݬ‬Ҿͳ͵Ζɿಋ‫ॴغ‬ཀྵͺ෾ࢆεητϞ͹Ҳͯ͹୉͘͵՟ୌͳ͵ͮͱ͕Εɾ͞ΗΝްིԿͤΖघ๑ͺଡ͚‫͠ڂݜ‬Ηͱ͏Ζ[2,3]ɿҲ๏ͲɾΰʖϞ͵ʹ͹ɾεϝϣϪʖεϥϱ͹ਜ਼֮੓ΓΕ΍ଐౕ͗༑઎͠ΗΖίʖηͲͺɾ࣎ؔ͹͖͖
Ζಋ‫غ‬ͺචགྷ͵͏ίʖη΍͍Ζɿ Ήͪɾ৖ॶͶΓͮͱ࣎ؔ͹ླྀΗΖଐౕ͗ҡ͵Ζড়݇ԾͲεϝϣϪʖεϥϱΝߨͮͪࡏͶɾ‫ڏͤࣖ͗ܧ‬ಊͳɾͨ͹݃Վਫ਼ͣΖ࣎‫ؔۯ‬ϏνʖϱͶͯ͏ͱͺ͞ΗΉͲ‫͠ڂݜ‬Ηͱ͕Δͥɾ‫ັڷ‬਄͏ɿ

1.2. ‫ڂݜ‬͹໪దͳຌߚ͹ߑ੔઴ߴͲफ़΄ͪΓ͑͵ɾ‫ؔۯ‬͹৖ॶͶΓͮͱ‫ࢋܯ‬ब‫͗غ‬ҡ͵Ζয়‫Ͳڱ‬εϝϣϪʖεϥϱΝࣰߨͪ͢৖߻Ͷɾʹ͹Γ͑͵‫ݳ‬ে͗ਫ਼ͣಚΖ͹͖எ‫ݡ‬ΝಚΖͪΌ͹‫ેخ‬ద͵ ‫ͱ͢ͳڂݜ‬ɾຌߚͲͺɾΉͥ‫ؖ‬࿊‫ڂݜ‬Νफ़΄ɾୱ९͵೦ఽ಍ϠυϩΝଲেͶඉҲ༹͵‫ࢋܯ‬ब‫غ‬ͶΓͮͱεϝϣϪʖεϥϱΝࣰߨͪ͢৖߻͹‫ڏ‬ಊͶͯ͏ͱߡࡱͤΖɿ࣏Ͷ ɾਦ̏Ͳफ़΄ͪߑ੔ͳಋ
౵͹ড়݇ͲεϝϣϪʖεϥϱΝࣰߨͤΖٛࣇ‫ڧ؂‬Ν༽͏ͱɾ ഀಊ๏ఖࣞͳൕԢ֨ࢆ๏ఖࣞ
Νଲেͳͪ͢εϝϣϪʖεϥϱΝߨ͏ɾͨ͹݃Վͳ͢ͱਫ਼ͣͪ࣎‫ؔۯ‬ϏνʖϱΝࣖͤɿ

2. ‫ؖ‬࿊‫ڂݜ‬
2.1. ৖ॶͶΓͮͱҡ͵Ζ֨ࢆ‫਼ܐ‬Νઅఈͪ͢΍͹֨ࢆ๏ఖࣞΝଲেͳ͢ͱɾ‫ؔۯ‬దͶඉҲ༹͵֨ࢆ‫਼ܐ‬Ν࣍ͯ‫ܧ‬͹൅ఴΝ௒΄ͪ‫ش͗ڂݜ‬͖ͯଚࡑ͢ͱ͏Ζɿ[4]ͺ৖ॶͶΓͮͱҡ͵Ζ֨ࢆ‫਼ܐ‬Ν࣍ͯഖ࣯৏Ͷ͕͜ΖൕԢ֨ࢆ‫ܧ‬͹਒ߨഀմ͹‫ڏ‬ಊΝ֮೟͢ͱ͏Ζɿ[5]ͺɾਫ਼෼ൡ৫ͶΓΖ෾ාҮ֨୉Νઈ໎ͤΖ Fisher Ϡυϩ[6]ͳಋ༹͹֨ࢆ๏ఖࣞΝଲেͳ͢ͱɾਫ਼෼͹ൡ৫Ώਫ਼ଚͶͳͮͱ޹న͵৖ॶʤ֨ࢆ͢
Ώͤ͏৖ॶʥͳɾͨ͑Ͳ͵͏৖ॶʤ֨ࢆ͢Ͷ͚͏৖ॶʥ͗Ϡδ΢έয়Ͷଚࡑ͢ͱ͏Ζ͞ͳΝ૟ఈ͢ɾ‫ؔۯ‬Νଵয়Ͷۢ઀ͮͱɾͨΗͩΗ͹ଵͶҡ͵Ζ֨ࢆ‫਼ܐ‬Νઅఈͪ͢ড়݇ԾͶ͕
͜Ζɾմ͹৾Ζ෥͏Νմੵదʀ਼஍దͶ֮೟͢ͱ͏Ζɿ͞ΗΔ͹‫ڂݜ‬ͺɾεϝϣϪʖεϥϱ‫ؔۯ‬͹৖ॶͶԢͣͱҡ͵Ζড়݇અఈΝ͢ͱ‫ࢋܯ‬ΝͤΖ఼Ͳ ɾຌ‫ڂݜ‬͹खΕૌΊͳྪࣇ͢
ͱ͏Ζɿ͖͢͢ɾ͞ΗΔ͗ಝఈ͹‫྘ؔۯ‬Ү͹֨ࢆ‫਼ܐ‬Νଠ͹྘Үͳร͓Ζ͞ͳΝ૟ఈ͢ͱ͏Ζ͹Ͷଲ͢ɾຌ‫ڂݜ‬͹૟ఈͺɾͨ͹྘Ү͹‫ࢋܯ‬ब‫غ‬Νร͓Ζ͞ͳͲ͍Ζɿ

2.2. ιϩΨʖφϜφϱ͹‫ࢋܯ‬Νඉಋ‫غ‬దͶߨ͑΍͹[7]ͺɾ࣏̏‫ݫ‬͹ιϩΨʖφϜφϱϠυϩΝଲেͳ͢ͱɾ‫ؔۯ‬Ν‫͖ͯش‬͹ϔϫρέͶۢ઀ͮͪ৏Ͳɾ֦ϔϫρέ಼͹ιϩ͹‫ࢋܯ‬ͺಋ‫غ‬దͶߨ͏ͯͯɾϔϫρέ͟ͳ͹‫ࢋܯ‬͹ࣰߨν΢ϝϱήΝඉಋ‫غ‬Ͷࣰߨͪ࣎͢͹‫ڏ‬ಊΝ֮೟͢ͱ͏ΖɿΉͪɾ[8]ͺಋ͚࣏ͣ̏‫ݫ‬͹ιϩΨʖφϜφϱͶͯ͏ͱɾιϩ͹ߍ৿Νඉಋ‫͖ͯغ‬ϧϱξϞͶߨͮͪ৖߻͹‫ڏ‬ಊΝ֮೟͢ͱ͏
Ζɿ[9]ͺ࣏̐‫ݫ‬͹ιϩΨʖφϜφϱΝଲেͳ͢ͱ࣯ྖฯଚଉ͗੔ΕཱིͯΓ͑Ͷ͓ͪ͑͢Ͳɾ

t 91 tඉಋ‫غ‬ͶιϩΝߍ৿ͪ͢ࡏ͹৾Ζ෥͏Ν֮೟͢ͱ͏Ζɿ͞ΗΔ͹‫ڂݜ‬ͺɾસͱ͹ιϩ͹ߍ৿Νಋ‫غ‬దͶҲ‫ͤ৿ߍׇ‬Ζ͹Ͳͺ͵͚ඉಋ‫غ‬Ͷߨ఼͑Ͳ ɾຌ‫ڂݜ‬͹खΕૌΊͳྪࣇ͢ͱ͏
Ζɿͳ͚Ͷɾ[7]Ͳफ़΄ΔΗͱ͏Ζɾ‫྘ؔۯ‬ҮΝϔϫρέͶۢ઀Εɾϔϫρέ಼͹ιϩߍ৿ͺಋ‫غ‬దͶࣰߨͤΖߑ੔ͺຌ‫ڂݜ‬͹Հఈͳಋ༹Ͳ͍Ζɿ͖͢͢[7]Ͳͺɾຌ‫͗ڂݜ‬૟ఈͤΖΓ͑͵ɾ֦ϔϫρέ͗ͨΗͩΗ‫༙ݽ‬͹‫ࢋܯ‬ब‫غ‬Ν΍ͮͱಢཱིͶ‫ࢋܯ‬Ν਒ΌΖͳ͏͑ড়݇Ծ
Ͷ͕͜Ζ৾Ζ෥͏ͺࣖ͠Ηͱ͏͵͏ɿ

3. ೦ఽ಍๏ఖࣞΝଲেͳͪ͢ߡࡱຌߚͲͺҐ߳ɾεϝϣϪʖεϥϱ‫ؔۯ‬͹ۢ෾Νϔϫρέͳ‫΁ݼ‬ɿ֦ϔϫρέͺ‫ڠ‬௪͹γ΢θ͹֪ࢢഓ྽ͶΓͮͱ੔Εཱིͮͱ͏Ζɿϔϫρέ಼͹֪ࢢͺಋ‫غ‬దͶ‫ࢋܯ‬ʀߍ৿͠ΗΖ
͗ɾ֦ϔϫρέͺͨΗͩΗ‫༙ݽ‬͹࣎ؔब‫غ‬ͶΓͮͱ‫ࢋܯ‬ητρϕΝ‫܃‬Εศͤয়‫ڱ‬Νߡ͓Ζ ɿΉͥୱ९͹ͪΌͶࣞʤ1ʥͲࣖͤ‫ݫ࣏̏ؔۯ‬͹೦ఽ಍๏ఖࣞ͹εϝϣϪʖεϥϱΝߡࡱͤΖɿ߲‫ ߲ ݑ‬ଶ ‫ݑ‬ൌ߲‫ ݔ߲ ݐ‬ଶ(1)

ਦ 3ʁ৖ॶͶΓΕ‫ֶؔࢋܯ‬͹ҡ͵Ζ೦ఽ಍εϝϣϪʖεϥϱ

ਦ 3 Ͷࣖͤ௪Εɾ೦ഖ࣯Νන֪ͤࢢ‫ ͗ؔۯ‬2 ͯ͹ϔϫρέͶΓͮͱൔ෾Ͷ෾͖Ηͱߑ੔͠Ηͱ͕ΕɾͨΗͩΗ͹ϔϫρέ͗ЍHzɾЎ+] ͹‫ֶؔࢋܯ‬Ν࣍ͯͳͤΖɿΉͪɾഖ࣯͹ࠪ୼Ν೦͢ɾӊ୼Νྮ‫͢٭‬କ͜ɾ֦֪ࢢͶͺഖ࣯͹Իౕ֪͗೴͠ΗΖ΍͹ͳͤΖɿ
͞͞ͲɾЍ͗ЎΓΕ΍‫୼ۅ‬Ͷ୉͘͏૟ఈʤЍ>>ЎʥͲɾॵ‫غ‬য়ସ͗‫ؔۯ‬దͶҲ༹͵Իౕ͖Δ‫ࢋܯ‬Ν֋࢟ͪ࣎͢Ͷɾ‫ؔ࣎ࢋܯ‬͹‫ܨ‬գͶ൒ͮͱรԿͤΖմ͹‫ܙ‬য় ͹યҢΝਦ 4 ͶࣖͤɿΉͥɾॵ‫غ‬য়ସʤਦ̒͹ᶅʥ͖Δ‫ͻ͢ޛ࢟֋ࢋܯ‬Δ͚ͺ ࠪϔϫρέ͹ΊͲළൡͶ‫ࢋܯ‬η

ਦ 4ʁ೦ఽ಍εϝϣϪʖεϥϱ ͹༩଎

t 92 tτρϕ͗‫܃‬Εศ͠ΗΖͪΌɾ࣎ؔ‫ܨ‬գͶ൒ͮͱࠪ୼͗೦͠Η߶ԻͶ͵ΖɿЍ!!Ў ΝՀఈ͢ͱ͏Ζ͹Ͳ͞͹఼࣎Ͳͺӊϔϫρέ͹‫ࢋܯ‬ητρϕ͗Ήࣰͫߨ͠ΗͥɾԻౕรԿ͗ਫ਼ͣ
͵͏ɿࠪϔϫρέ͹ཱི৖Ͳͺɾ͞͹ؔɾࠪϔϫρέ಼͹ӊ୼‫ڧ‬ֆͺॵ‫غ‬஍Ͳ‫ݽ‬ఈ͠Ηͱ͏Ζ͹ͳಋ౵Ͳ͍ΖͪΌɾӊ୼͹Իౕͺఁ͏ΉΉͲ͍Ζʤਦ̒͹ᶆʥɿ͖͞͞Δॉ෾Ͷ࣎ؔ͗‫ܨ‬գͤΖͳɾӊϔϫρέ΍‫ࢋܯ‬ητρϕ͗‫܃‬Εศ͠Ηɾ݃Վͳ͢ͱӊϔϫρέ಼͹ӊ୼ͺྮ‫͠٭‬ΗͱԻౕ͗Ծ͗Ζɿಋ࣎Ͷɾӊϔϫρέ಼͹ࠪ୼‫ڧ‬ֆͺࠪϔϫρέ͖Δླྀ೘͢ͱ͚
Ζ೦͹Ӫ‫ڻ‬Νण͜ͱԻౕ͗৏͗ΖɿΉͪɾॉ෾ௗ͏࣎ؔऊౕͲଌ͓Ζͳɾࠪϔϫρέ͹ཱི৖͖ΔΊͱࠪϔϫρέ಼͹ӊ୼‫ڧ‬ֆͺࣙ༟‫ڧ‬ֆͳࣇͪয়‫͵ͳڱ‬Εɾࠪϔϫρέ಼͹ӊ୼͹Իౕ΍৏͗ͮͱ͏͘ɾ࠹शదͶͺਦ 4 ͹ᶇͲࣖͤฑߩয়ସͶཚͬ஥͚ɿਦ 4 ͺЍ͗ЎΓΕ΍‫୼ۅ‬Ͷ୉͘͏ίʖηΝ૟ఈͪ͢΍͹Ͳ͍Ζ͗ɾЍΏЎ͹஍ɾΉͪɾ‫ؔۯ‬͹෾ׄ‫਼ݺ‬Ώ෱Ͷ͖͖ΚΔͥॉ෾࣎ؔ͗‫ܨ‬գͪ͢‫ޛ‬͹݃Վͺಋ༹͵΍͹ͳ͵ΖɿΉͪɾ͞Ηͺ‫ؔۯ‬దͶҲ༹͵‫ࢋܯ‬ब‫غ‬Ν࣍ͯҲൢద͵εϝϣϪʖεϥϱΝߨͮͪ࣎͹ฑߩ য়ସͲ΍͍Ζɿͪ͗ͮ͢
ͱɾঙ͵͚ͳ΍࣏̏‫ݫ‬೦ఽ಍๏ఖࣞ͹࣎ؔ൅ఴεϝϣϪʖεϥϱͶΓͮͱ‫ٽ‬ΉΖฑߩয়ସͺɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬͹Ӫ‫ڻ‬Νण͜͵͏ͳ͏͓ΖɿΉͪɾ‫ؔۯ‬͹࣏‫ݫ࣏̐͗ݫ‬Ώ࣏̑‫Ͳݫ‬͍ͮͱ΍ɾ͍Ζ‫ڧ‬ֆড়݇Ͷ͕͜Ζ೦ఽ಍๏ఖࣞ‫ܧ‬͹ฑߩয়ସͺҲқͶఈΉΖͪΌ ɾ࣎ؔ͗ॉ෾Ͷ‫ܨ‬գͪ࣎͢͹য়ସͺඉҲ༹͵‫ࢋܯ‬ब‫غ‬͹Ӫ‫ڻ‬Νण͜͵͏ͳࢧΚΗΖ ɿ

4. ഀಊ๏ఖࣞɾൕԢ֨ࢆ๏ఖࣞΝଲেͳͪ͢εϝϣϪʖεϥϱ઴হͲफ़΄ͪ೦ఽ಍๏ఖࣞͺɾ‫ܧ‬͹ฑߩয়ସ͗‫ࢋܯ‬ब‫غ‬ͶғΔͥҲқͶఈΉΖͪΌɾ‫ܯ‬ࢋब‫͗غ‬ඉҲ༹Ͳ͍ͮͱ΍ɾҲ༹Ͳ͍Ζ৖߻ͳർֳ͢ͱ࣎ؔ‫ܨ‬գͪ͢‫ޛ‬͹য়ସͶҩ͏ͺໃ͏͞ͳΝफ़΄ͪɿ͞ΗͶଲ͢ͱɾഀಊ๏ఖࣞ‫ܧ‬ΏൕԢ֨ࢆ๏ఖࣞ‫ܧ‬ͺɾ෵਼͹մ͗ଚࡑͤ
ΖͪΌɾफ଍ͤΖմΏɾմͶफ଍ͤΖգోգఖ͗ɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬ͶΓͮͱʹ͹Γ͑͵Ӫ‫ڻ‬Νण͜Ζ͹͖༩଎Ͳ͘͵͏ɿͨ͞ͲɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬Ν࣍ͯ෾ࢆεϝϣϪʖν৏Ͳ͞ΗΔ͹‫ܧ‬ΝࣰࡏͶۨಊ͢ɾͨ͹‫ڏ‬ಊΝ֮೟ͪ͢ɿ

4.1. εϝϣϪʖεϥϱ‫ڧ؂‬
ਦ 5 Ͷɾࣰ‫ݩ‬Νߨͮͪٛࣇ෾ࢆεϝϣϪʖν͹֕གྷΝࣖͤɿ֦‫ࢋܯ‬όʖχͺ‫ؔۯ‬৏͹‫ݽ‬༙͹ϔϫρέΝฯ࣍͢ɾͨΗͩΗ͗ಢཱིͶ‫ࢋܯ‬ητρϕΝ஠ࣰ࣏ߨͤΖɿຌཔ͹෾ࢆεϝਦ 5ʁεϝϣϪʖεϥϱߑ੔ ʤਦ̏͹εητϞΝໝͪٛ͢ࣇ‫ڧ؂‬ʥ

t 93 tϣϪʖν͹‫ࢋܯ‬όʖχͺɾਦ̏Ͷࣖͪ͢Γ͑Ͷพʓ͹‫ؽࢋܯ‬ͶΓͮͱಊࡠ͢ɾόʖχؔ͹௪৶ͺϋρφϭʖέΝղ͢ͱߨ͑͞ͳΝ૟ఈ͢ͱ͏Ζ͗ ɾࠕյͺ‫ࢋܯ‬ब‫غ‬͹Ӫ‫ڻ‬͹ΊΝ֮೟ଲেͳͪͪ͢Όɾ֦‫ࢋܯ‬όʖχͺ 1 ͯ͹ηϪρχʤ‫ॴࢋܯ‬ཀྵࣰߨ͹ୱҒʥͳ͢ͱࣰૹ͢
ͪ৏Ͳ 1 ୈ͹‫Ͳ಼ؽࢋܯ‬ಊࡠͦͪ͠ɿΉͪɾόʖχؔ͹௪৶ͺϟϠϨΝղ͢ͱߨ͑͞ͳͲ
ϋρφϭʖέ௪৶ͶགྷͤΖ࣎ؔ͹Ӫ‫ڻ‬Νഋঈͪ͢ɿ‫ؔۯ‬ͺ 135ʹ135 ‫ݺ‬͹֪ࢢͶΓͮͱߑ੔͢ɾͨΗΔΝ֪ࢢয়Ͷ‫ ͫ͏ܪ‬9 ͯ͹‫ࢋܯ‬όʖχʤηϪρχʥͶׄΕ౲ͱɾεϝϣϪʖεϥϱΝด྽ࣰߨͪ͢ɿ֦όʖχͺ 45ʹ45 ͹֪ࢢϔϫρέΝฯ࣍ͦͪ͠ɿΉͪɾͨΗΔ͹ߍ৿ब‫غ‬Νਦ 6 Ͷࣖͤ௪Ε͹ϏνʖϱͲ݀ఈͪ͢ɿ
ਦ 6 Ͷ͕͜Ζࠉ͏ϔϫρέͺɾപ͏ϔϫρέ͹‫ࢋܯ‬όʖχΓΕ΍‫ࢋܯ‬ब‫غ‬Νௗ͚ͤΖ͞ͳΝࣖ͢ͱ͏Ζɿࠕյɾࠉ͏ϔϫρέͺɾപ͏ϔϫρέ͹ 4 ഔ͹‫ࢋܯ‬ब‫ͪ͢ͳغ‬ɿͯΉΕɾࠉ͏ϔϫρέ͗ 1 յ‫ࢋܯ‬ητρϕΝࣰߨͤΖؔͶɾപ͏ϔϫρέͺฑ‫ ͱ͢ۋ‬4 յ͹‫ࢋܯ‬ητρϕΝࣰߨͤΖ͞ͳͶ͵Ζɿ͵͕ɾ‫ݺ‬ʓ͹ηϪρχͺɾຌཔͺಢཱིͪ͢‫ؽࢋܯ‬৏Ͳҡ͵Ζϕϫιηͳ͢ͱಊࡠͤΖ͞ͳΝ૟ఈ͢ͱ͏ΖͪΌ ɾηϪρχؔ͹ಋ‫غ‬ͺߨͮͱ͏͵͏ɿͨ͹ͪΌɾ‫ࢋܯ‬ητρϕࣰߨ͹յ਼ർིʤ1:4ʥͺ͍͚ΉͲ໪҈Ͳ͍ΕɾηϪρχॴཀྵ͹਒ṁয়‫ڱ‬ͶԢͣͱऑ‫ͤݰଁױ‬ΖɿΉͪɾ֦ηϪρχͺ‫ࢋܯ‬ητρϕΝࣰߨͤΖͪ;Ͷ ɾͨ͹఼࣎͹ϔϫρέ‫ڧ‬ֆͶ͕͜Ζ֪ࢢ͹য়ସ஍ΝۛંηϪρχ΃௪எͤΖɿҐ߳ɾࠉ͏ϔϫρέΝஙԈϔϫρέɾപ͏ϔϫρέΝ௪৙ϔϫρέͳ‫΁ݼ‬ɿεϝϣϪʖεϥϱΝࣰߨͪ͢‫ؽࢋܯ‬͹੓೵ͺ CPU1.8GHz 4 αΠʤ8 ࿨ཀྵϕϫιργʥ,ϟϠϨ 8GB Ͳ͍ΖɿεϝϣϪʖεϥϱ͹ϕϫιηͺ Java Ͷͱࣰૹͪ͢ɿԍࢋͶ GPU ͺ༽͏ͱ͏͵͏ɿ

ਦ 6ʁஙԈϔϫρέ͹ഓ஖Ϗνʖϱ

4.2. ഀಊ๏ఖࣞΝଲেͳͪ͢εϝϣϪʖεϥϱ઴ߴͲफ़΄ͪεϝϣϪʖεϥϱ‫ڧ؂‬৏Ͳɾࣞʤ2ʥͶࣖͤ 2 ࣏‫ݫ‬͹ഀಊ๏ఖࣞ͹࣎ؔ൅ఴΝ‫ͪ͢ࢋܯ‬ɿεϝϣϪʖεϥϱ͹‫ࢋܯ‬๏ࣞͺࠫ෾๑Ͳ͍Ζ ɿ۫ରదͶͺࣞʤ2ʥΝ཯ࢆԿͪࣞ͢ʤ3ʥͶΓͮͱ݀ ൌ ͳͲି଻ ͳ͕͏ͱɼ֪ࢢΝߍ৿ͤΖ‫ࢋܯ‬ητρϕΝ஠ࣰ࣏ߨͪ͢ɿ
ࣞʤ3ʥ಼͹శ͓࣊݅ǡ ݆ͺ֪ࢢ͹࠴ඬΝɾ‫ݐ‬ͺ࣎ؔητρϕΝන͢ͱ͏Ζɿt 94 t߲ଶ‫߲ ݑ‬ଶ‫ݑ‬ൌ߲‫ ݐ‬ଶ ߲‫ ݔ‬ଶ

(2)

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‫ݑ‬௜ǡ௝ൌ ʹ‫ݑ‬௜ǡ௝െ ‫ݑ‬௜ǡ௝൅ ݀ሺ‫ݑ‬௜ିଵǡ௝൅ ‫ݑ‬௜ାଵǡ௝൅ ‫ݑ‬௜ǡ௝ିଵ൅ ‫ݑ‬௜ǡ௝ାଵെ Ͷ‫ݑ‬௜ǡ௝ሻ(3)‫ڧ‬ֆড়݇ͺब‫ڧغ‬ֆড়݇ͳ͢ɾॵ‫غ‬஍ͳ͢ͱ‫ؔۯ‬దͶҲ༹͵஍ʁ0 Νઅఈͪ͢৏Ͳɾ‫ؔۯ‬͹஦ԟͶҒ஖ͤΖ֪ࢢͶଲ͢ͱਜ਼‫ݯ‬ഀͶΓͮͱ৾ಊΝ༫͓କ͜ͱεϝϣϪʖεϥϱΝۨಊͪ͢ɿਜ਼‫ݯ‬ഀ͹ब‫غ‬ͺɾͨ͹ϔϫρέͶ͕͜Ζ‫ࢋܯ‬ητρϕब‫غ‬ൈ ͳͲଷͳ͢ͱ༫͓ͪɿ‫ؔۯ‬஦ԟ͗௪৙ϔϫρέ͹৖߻ͺɾͨ͞Ͳ༫͓ΔΗΖਜ਼‫ݯ‬ഀ͹ब‫غ‬ͺɾஙԈϔϫρέ͹ཱི৖͖ΔͤΖͳ༁ 1/4 ͳ͵Εɾ‫ٱ‬Ͷ‫ؔۯ‬஦ԟ͗ஙԈϔϫρέ͹৖߻ͺɾ௪৙ϔϫρέ͹ཱི৖͖Δͺ༁ 4 ഔͳ͵Ζɿ݃Վͳߡࡱ
ਦ 7 ͶεϝϣϪʖεϥϱ͹݃ՎΝࣖͤɿ֦ߨͶஙԈϔϫρέ͹ഓ஖ϏνʖϱΝɾ֦྽Ͷͨ Η ͩ Η ͹ Ϗ ν ʖ ϱ Ͷ ͕ ͜ Ζ ࣎ ؔ ‫ ܨ‬գ Ͷ ൒ ͑ մ ͹ ‫ ܙ‬য় Ν ඵ ժ ͢ ͪ ΍ ͹ Ͳ ͍ Ζ ɿ մ ‫ ܙ‬য়ͺ
135ʹ135 ϒέιϩ͹໎ౕժ଀Ͳ͍Εɾ֦ϒέιϩ͹໎ౕͺ‫ݑ‬͹஍ͶԢͣͱ݀Όͱ͏Ζɿ͏ͥΗ͹݃Վ΍ɾεϝϣϪʖεϥϱ࣎ؔ͹‫ܨ‬գͶ൒ͮͱ࠹शదͶͺఈ৙ഀ͗ਫ਼੔͠Ηͪɿఈ৙ഀ͹Ϗνʖϱͳ͢ͱͺɾഀ‫ͱ͢ͳݱ‬ਜ਼‫ݯ‬ഀΝ༫͓ͪ‫ؔۯ‬͹஦ԟ͹ϔϫρέ͗ஙԈϔϫρέ͖௪৙ϔϫρέ͖Ͳ෾ྪͲ͘Ζɿ‫ؔۯ‬஦ԟ͗௪৙ϔϫρέͲ͍Ζʤഀ‫͗ݱ‬௪৙ϔϫρέͶ͍Ζʥ৖߻஦ԟͲ൅ਫ਼ͪ͢ഀ͹ഀௗ͗ɾஙԈϔϫρέͲͺ୻͚͵Ζ͞ͳ͖ΔɾஙԈϔϫρέͲͺ௪৙ϔϫρέͳർֳ͢ͱࡋ͖͵ഀ͗ଚࡑ͢ͱ͕ΕɾͨΗΝ໎֮Ͷ໪ࢻͤΖ͞ͳ͗Ͳ͘Ζʤਦ
7 ͹ B,E,F,I,K,L ߨʥɿΉͪɾஙԈϔϫρέͲਫ਼ͣΖഀ͹‫ܙ‬য়ͺ௪৙ϔϫρέͳ͹ં͢๏Ͳ
รԿͤΖ͞ͳ͗෾͖Ζɿྭ͓ͻਦ 7 ͹Ϗνʖϱ B ͲͺஙԈϔϫρέͺ௪৙ϔϫρέͳೈ๼Ͳ͖͢ં͢ͱ͕Δͥɾഀ͗ͨΗͶԌͮͱࡋௗ͚ଚࡑ͢ͱ͏Ζ͞ͳ֮͗೟Ͳ͘Ζʤਦ 7 ͹ Bߨ 32,64 ྽ʥ ɿ‫ؔۯ‬஦ԟ͗ஙԈϔϫρέͲ͍Ζʤഀ‫͗ݱ‬ஙԈϔϫρέͶ͍Ζʥ৖߻஦ԟͲ൅ਫ਼ͪ͢ഀ͹ഀௗͺɾ௪৙ϔϫρέͲͺௗ͚͵Ζ͞ͳ͖Δɾ௪৙ϔϫρέͲͺ ഀௗ͹୉͘͵ഀ͗ਫ਼੔͠ΗΖɿΉͪɾ͞͹ഀ͹Ӫ‫ڻ‬Ν‫ٱ‬Ͷण͜ͱஙԈϔϫρέ͹ഀ ௗ΍ௗ͚͵Εɾॉ෾͵࣎ؔ͗‫ܨ‬գͤΖͳɾஙԈϔϫρέͳ௪৙ϔϫρέ͹໪ࢻͶΓΖۢพͺͲ͘͵͚͵Ζɿt 95 tਦ 7ʁഀಊ๏ఖࣞ͹εϝϣϪʖεϥϱ݃Վt 96 t4.3. ൕԢ֨ࢆ๏ఖࣞΝଲেͳͪ͢εϝϣϪʖεϥϱൕԢ֨ࢆ‫ܧ‬ͺɾඉҲ༹͵‫ؔۯ‬ϏνʖϱΝ࣍ͯฑߩմ͗ଚࡑ͢ͱ͏ Ζ[10]ɿࠕյͺൕԢ֨ࢆ‫ܧ‬͹஦Ͳ΍ಝͶଡ༹͵մΝ࣍ͯ͞ͳͲஎΔΗͱ͏Ζࣞʤ4ʥͶࣖͤ 2 ࣏‫ݫ‬͹ GrayScottϠυϩ[11,12]͹࣎ؔ൅ఴΝ‫ͪ͢ࢋܯ‬ɿεϝϣϪʖεϥϱͺ઴ߴಋ༹Ͷɾࠫ෾๑ͶΓͮͱ‫ܯ‬ࢋΝߨͮͪɿ֪ࢢߍ৿͹ͪΌ͹཯ࢆࣞͺࣞʤ5ʥͶࣖͤ௪ΕͲ͍Εɾ‫ ܨ‬ൌ ͲǤͲͶǡ ݇ ൌ ͲǤͲͷͻǡ ݀ ൌͲǤͲͳǡ ݇ ൌ ͲǤͲͳǡ ‫ܦ‬௨ ൌ ͳͲିହǡ ‫ܦ‬௩ ൌ ʹ ൈ ͳͲିହͳ͕͏ͪɿ
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(4)

(5)

‫ڧ‬ֆড়݇ͺब‫ڧغ‬ֆড়݇ͳ͢ɾ‫ؔۯ‬͹஦ԟͶҒ஖ͤΖ֪ࢢሺ݅௖ ǡ ݆௖ ሻΝ஦ৼͳ͢ͱਫ਼੔ͪ͢ΪΤη‫਼݂ؖ‬ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൌ ͳͲ ൈ ሼെሺ‫ ݔ‬െ ݅௖ ሻଶ െ ሺ‫ ݕ‬െ ݆௖ ሻଶ ሽΝॵ‫غ‬஍ͳ͢ͱ༫͓ͪɿ݃Վͳߡࡱ
ਦ 8 ͶεϝϣϪʖεϥϱ͹݃ՎΝࣖͤɿ઴ߴಋ༹Ͷɾ֦ߨͶஙԈϔϫρέ͹ഓ஖ϏνʖϱΝɾ֦྽ͶͨΗͩΗ͹ϏνʖϱͶ͕͜Ζ࣎ؔ‫ܨ‬գͶ൒͑մ͹‫ܙ‬য়Νඵժͪ͢΍͹Ͳ͍Ζ ɿΉͪɾϒέιϩ͹໎ౕͺ‫ݑ‬͹஍ͶԢͣͱ݀Όͱ͏Ζɿ઴ߴͲ͹ഀಊ๏ఖࣞͺɾ೘ྙͳ͢ͱਜ਼‫ݯ‬ഀΝ༫͓କ͜ͱ͏ͪͪΌɾ࣎ؔ‫ܨ‬գͳͳ΍ͶรԿ͢͵͚͵Ζฑߩմͺଚࡑ͢͵͖ͮͪ͗ɾ͞͞Ͳଲেͳͪ͢‫ܧ‬Ͷͺฑߩմ͗ଚࡑ͢ɾ‫ࢋܯ‬ητρϕΝॉ෾Ͷ॑͸ΖͳɾͨΗҐ৏࣎ؔ‫ܨ‬գ͢ͱ΍รԿ͢͵͚͵Ζয়ସ͗ಚΔΗΖɿ Ήͪɾ઴হͲफ़΄ͪୱ९͵೦ఽ಍๏ఖࣞͺɾฑߩմͳ͢ͱखΕ͓Ζয়ସͺ 1 ͯͫ͜Ͳ͍ͮͪ
ͪΌɾඉҲ༹͵‫ࢋܯ‬ब‫ͱ͍ͮͲغ‬΍ɾॉ෾Ͷ࣎ؔ͗‫ܨ‬գͪ͢‫ޛ‬͹݃ՎͶรΚΕͺ͵͖ͮͪɿ͖͢͢ɾ͞͞Ͳଲেͳͪ͢‫ܧ‬ͺɾฑߩմ͗ଡ༹Ͷଚࡑ͢ͱ͕ΕɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬͹Ӫ‫ڻ‬Νण͜ͱɾ࣎ؔ‫ܨ‬գͶ൒ͮͱ౺ୣͤΖয়ସ΍รԿ͢ͱ͏Ζ༹ࢢ͗Κ͖Ζɿմ͹Ϗνʖϱͳ͢ͱͺɾ઴ߴ͹ഀಊ๏ఖࣞΝଲেͳͪ͢εϝϣϪʖεϥϱ݃Վ͹Γ͑Ͷ ɾஙԈϔϫρέͳ௪৙ϔϫρέ͹ؔͲմ͹‫ܙ‬য়͹ഀௗͶ୉͘͵ҩ͏ͺड़Ζ͞ͳͺ͵͖ͮͪ ɿ͖͢͢ɾ‫ࢋܯ‬͹գఖͲɾ௪৙ϔϫρέͲϏνʖϱ‫ܙ‬੔͗ଐ͚਒ߨͤΖͪΌ ɾΉͥ௪৙ϔϫρέͶ͕͏ͱϏνʖϱ͗ਫ਼੔͠Ηɾͨ͹‫ޛ‬ͶஙԈϔϫρέͲ͹Ϗνʖϱਫ਼੔͗ɾ‫ۯ‬പ྘ҮΝດΌΖΓ͑Ͷ਒ߨͤΖ༹ࢢ͗؏ࡱͲͪ͘ɿ͞͹ͳ͘ɾ‫ۯ‬പ྘Ү͹‫ܙ‬য়ͶԌͮͱϏνʖϱਫ਼੔͗͵͠ΗΖͪΌɾ‫ʹ͗ܧ‬͹Γ͑͵գఖΝḹͮͱͨ͹ฑߩয়ସͶ౺ୣͪ͢͹͖ɾ͏Κͻգోգఖ͹‫֮͗੽ܙ‬೟Ͳͪ͘ɿൕԢ֨ࢆ‫͗ܧ‬ਫ਼੔ͤΖ‫ؔۯ‬Ϗνʖϱͺɾ྘ҮͶଲͤΖనԢ੓ʀ੖྽੓Ν༙͢ͱ͏Ζ͞ͳ͗எΔΗͱ͕Ε[13,14]ɾ͞͹‫੽ܙ‬ͺ͞͹੓࣯ͶΓΖ΍͹Ͳ͍
Ζͳߡ͓ͱ͏Ζɿ

t 97 tਦ 8ʁൕԢ֨ࢆ๏ఖࣞ͹εϝϣϪʖεϥϱ݃Վt 98 tΉͳΌ‫ؔۯ‬దͶඉҲ༹͵‫ࢋܯ‬ब‫غ‬Ν࣍ͯεϝϣϪʖεϥϱͶ‫ͤؖ‬Ζߡࡱͳࣰ‫ݩ‬Νߨͮͪ ɿ೦ఽ಍๏ఖࣞͶͯ͏ͱͺɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬͹Ӫ‫ڻ‬Νण͜͵͏͞ͳΝߡࡱͪ͢ ɿഀಊ๏ఖࣞͶͯ͏ͱͺɾεϝϣϪʖεϥϱ͹݃ՎɾඉҲ༹͵‫ࢋܯ‬ब‫غ‬ͶΓͮͱಚΔΗΖմ͹ఈ৙ഀ͹Ϗνʖϱ͗୉͚͘ҡ͵ͮͪɿΉͪɾͨ͹ఈ੓ద͵੓࣯ͺഀ‫͗ݱ‬௪৙ϔϫρέ͖ஙԈϔϫρέ͹ʹͬΔͶҒ஖ͤΖ͖Ͳ୉Ή͖͵෾͜Ζ͞ͳ͗Ͳͪ͘ɿൕԢ֨ࢆ๏ఖࣞͶͯ͏ͱͺɾಚΔ
ΗΖ‫ؔۯ‬ϏνʖϱͶఈ੓ద͵ҩ͏ͺਫ਼ͣ͵͖ͮͪɿ͖͢͢ɾͨ͹ϏνʖϱͶ౺ୣͤΖΉͲ͹գఖ͹‫੽ܙ‬Ν‫ݡ‬Ζ͞ͳ͗Ͳͪ͘ɿ

ࢂߡช‫ݛ‬
[1]

Guan,

Q.:

pRPL:

an

open-source

general-purpose

parallel

Raster

Processing

programming Library, SIGSPATIAL Special, Vol. 1, pp. 57 -62 (2009).
[2]‫ ݒ‬෨ र ‫ݡ‬, ‫ ޳ ؖ‬ஒ ࢜. (1998). ‫ ༙ ڠ‬ϟ Ϡ Ϩ ‫ ؽ ࢋ ܯ‬Ͷ ͕ ͜ Ζ ‫ ॶ ۃ‬ಋ ‫ ߑ ؽ غ‬, ৚ ๅ ॴ ཀྵ ָ ճ‫ڂݜ‬ๅࠄ(HPC)[3]Ո ੇ ඛ, ࠦ ౽ ๗ ध, એ ཁ ࣐. (2015), ܲ ྖ Ͳ ப ে ౕ ͹ ߶ ͏ ড় ݇ ෉͘ ώ Ϩ Π ಋ ‫ ͨ ͳ غ‬͹ࣰૹ๏๑. ৚ๅॴཀྵָճ࿨ชࢿϕϫήϧϝϱήʤ PROʥ

[4]

Hideo Ikeda, Shin-Ichiro Ei, Front dynamics in heterogeneous diffusive media, Physica
D: Nonlinear Phenomena, Volume 239, Issue 17, 2010, Pages 1637 -1649[5]॑ఈ ೈ಺ࢢ, ৷೘ͳఽ೽͹਼ཀྵਫ਼ସָ , ౨‫ښ‬୉ָड़൝ճ, 1992

[6] Fisher, R.A. (1937) The Wave of Advance of Advantageous Genes. Annals of Eugencies, 7,355-369[7]

Sipper, Moshe & Tomassini, Marco & Capcarrere, M.. (1998). Evolving Asynchronousand Scalable Non-uniform Cellular Automata.

[8]

Kanada, Yasusi. (1997). The Effects of Randomness in Asynchronous 1D Cellular
Automata.

[9]Suzudo, Tomoaki. (2004). ඉಋ‫غ‬ιϩΨʖφϜφϱ͹૓൅దϏνʖϱ‫ܙ‬੔ . ుࢢ৚ๅ௪৶ָճ ඉત‫ܙ‬໲ୌ‫ڂݜ‬ճ

[10] A. M. Turing, The Chemical Basis of Morphogenesis, Philosophical Transactions of theRoyal Society, 1952.
[11] P. Gray and S.K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tankreactor: Isolas and other forms of multistability, Chem. Eng. Sci. Vol.38 (1983), 29 -43.
[12] P. Gray and S.K. Scott, Autocatalytic reactions in the isothermal, con tinuous stirred tankreactor: oscillations and instabilities in the system A+2B ˢ 3B ˢ C, Chem. Eng. Sci.
[13] H. Notsu, D. Ueyamab and M. Yamaguchi, Applied Mathematics Letters 26, 201 (2013).
[14] ྵ໨ ༺ฑ,߶ࢃ ‫ي‬༡,‫ݫ‬ஓ үࢢ,છҬ ఫ໷. (2005). ͢Ήʀ൙఼ժ଀Ϗνʖϱ͹र෰Νߨ͑ൕԢ֨ࢆϠυϩͳͨ͹ LSI Կ,ుࢢ৚ๅ௪৶ָճ࿨ชࢿ A ‫ેخ‬ʀ‫ڧ‬ֆ

t 99 tt 100 t࿨ช‫ܙ‬͹Ռָճࢿ ୊ 35 ‫ ת‬୊ 2 ߺཱིରӫ଀ࢻ೟࣎Ͷ͕͜Ζࢻતٌ੽Ϗνʖϱͳ॑ৼಊ༵Ϗνʖϱ͹‫ܐؖ‬੓ঘ໼࿉ଢ࿢ ฑీཾ߀ ߶ీभधෳҬ୉ָ୉ָӅ޽ָ‫ڂݜ‬ՌෳҬ‫ݟ‬ෳҬࢤช‫ ښ‬--WDNDGD#X-IXNXLDFMS

5HODWLRQVKLSEHWZHHQ3DWWHUQVRIWKH(\H0RYHPHQWDQGWKH
%RG\6ZD\:KLOH9LHZLQJD'9LGHR&OLSV
5HQWDUR2QR7DND\XNL+LUDWD+LURNL7DNDGD*UDGXDWH6FKRRORI(QJLQHHULQJ8QLYHUVLW\RI)XNXL--%XQN\R)XNXL(2021 ೧ 1 ݆ 14 ೖण෉ɾ2021 ೧ 1 ݆ 25 ೖणཀྵ)Abstract: In recent years, the development of video technology has increased the chance ofviewing stereoscopic films on media such as televisions and movie theaters. As the viewing of
3D video has become more commonplace, symptoms such as visually induced motion sickness(VIMS) and eye fatigue have been reported. In a previous study, post peripheral tracking wasshown to influence the equilibrium function compared to post tracking of a 3D video clip.
However, this result may depend on the experimental environment. In this study, weinvestigate the relationship between patterns of the eye movement and the body sway while
viewing a 3D video clips. Our results show that post peripheral viewing increases gain. Thissuggests that post peripheral viewing tends to accumulate fatigue.
Keywords: 3D video clips, Visually induced motion sickness (VIMS), Eye movement, Bodysway pattern, Transfer function analysis

1. ຌ࿨ช͹໪ద
ۛ೧ɼ3DCG ٗढ़͹ඊ༄ద͵਒ิͶΓΕɼཱིରӫ଀͗ਐۛ͵΍͹Ͷ͵Ζͳͳ΍Ͷɼϐφ͗͞ΗΉͲͶ‫ͳͪ͢͞ݩܨ‬͹͵͏ࢻְ࢙ܻΝण͜Ζ͞ͳ͗ड़པΖ࣎େͶ͵ͮͪɽ 2010
೧ͺ 3D ‫ݫ‬೧ͳ‫ͻݼ‬Ηɼ3D ӫ଀੣඾͗ࢤ৖Ͷ߁ΉΕ࢟ΌͪɽΉͪɼ৿ͪͶ 2016 ೧ͺ VR‫ݫ‬೧ͳ‫ͻݼ‬Ηɼྡ৖‫״‬͹߶͏ӫ଀͗ఴ֋͠Η͍ͯͯΖɽ͞͹Γ͑͵੣඾͹෕‫ٶ‬ͺɼ‫ֺޚ‬෾໼ͶͳʹΉΔͥɼҫྏΏ‫گ‬үɼෳࢳ͵ʹଡ‫ز‬ͶΚͪΖ [1][2]ɽͨ͹Ҳ๏Ͳɼ‫ء‬ൾ࿓Ώᅇృ‫״‬ɼ਴͏͵ʹ͹ӫ଀਴͏ͳ‫ͻݼ‬ΗΖ෈չ͵঳য়͗Ӏً͘͞͠ΗΖ͵ʹɼ݊߃৏͹ѳӪ‫ݔ͗ڻ‬೨͠Ηͱ͏Ζ[3]ɽͨ͞Ͳɼ༹ʓ͵ਫ਼ର৶ߺ͖Δӫ଀਴͏Ν඲ՃͤΖ‫͠͵͗ڂݜ‬Ηͱ͏Ζ[4][5]ɽ
ӫ଀਴͏Ͷͯ͏ͱਫ਼ཀྵࢨඬΝ༽͏ͪఈྖద͵඲Ճ๏๑͹Ҳͯͳ͢ͱɼ॑ৼಊ༵‫͗ࠬݗ‬‫͝ڏ‬ΔΗΖ[6]ɽ॑ৼಊ༵‫Ͳࠬݗ‬ͺɼඅ‫͗ंݩ‬଎ఈ‫ح‬͹৏ͶཱིҒͪ͢য়ସ͹॑ৼҒ஖Ν‫ى‬
࿧ͤΖɽ͞͹๏๑ͺɼཱིରӫ଀ࢻ೟࣎͹ӫ଀ͶΓΖରฑߩ‫΃ܧ‬͹Ӫ‫ڻ‬ΝఈྖదͶ඲ՃͤΖ͹Ͷ༙ްͲ͍Ζɽ઎ߨ‫ڂݜ‬Ͷ͕͏ͱͺɼӫ଀͹ࢻ೟๏๑Ͷ஭໪͠Ηͱ͕Εɼ௧ॊࢻͶt 101 tർ΄बวࢻ͹๏͗ରฑߩ‫ܧ‬ͶӪ‫ڻ‬Ν‫͠ࠨࣖ͗ͳͤ͞·ٶ‬Ηͪ[7]ɽ͖͢͢ɼࣰ‫ڧ؂ݩ‬Ͷғଚ͢ͱͨ͹ܑ޴͗ΊΔΗ͵͏͞ͳ΍͍Εɼӫ଀਴͏͹‫ؽ‬঄͹৆ࡋΝմ໎ͤΖ͞ͳ͗‫ٽ‬Ό
ΔΗͱ͏Ζɽ
ϐφ͹ରฑߩͺɼ༹ʓ͵‫ְ״‬৚ๅ͹౹߻ͶΓͮͱฯ࣍͠Ηͱ͏ΖɽकͶɼᶅ઴ఋ‫͖ح‬ΔಚΔΗΖՅଐౕ৚ๅɼᶆࢻְ৚ๅɼᶇର੓‫ְ״‬৚ๅ͹ 3 ‫ܧ‬౹Ͳ͍Ζɽ͞ΗΔ͹೘ྙ৚ๅ͗ɼൕࣻ‫ܧ‬Ώ߶࣏೶Ͳ͹৚ๅॴཀྵΝ‫ͱܨ‬౹߻͠Ηͱɼड़ྙ‫΃ܧ‬΍ͪΔ͠ΗΖ [8]-[11]ɽ
Edwards ͹ๅࠄͶΓΖͳɼࢡ੐੏‫ޜ‬Ͷ‫ͤؖ‬Ζ৚ๅ͹͑ͬɼࢻְ৚ๅͺ 50%ఖౕΝઐΌΖͳๅࠄ͢ͱ͏Ζ[12]ɽΉͪɼࢻְ৚ๅ͗ܿཚͪ͢য়ସͲ͹ࢡ੐҈ఈ੓ͺɼࢻְ৚ๅ͹೘
ྙ͍͗Ζ৖߻ͳർ΄ɼ20-50%ఖౕఁԾͤΖ͞ͳ͗எΔΗͱ͏Ζ[13][14]ɽͨ͹ͪΌɼड़ྙ‫ͱ͢ͳܧ‬͹ࢡ੐ң࣍੏‫ޜ‬ͺࢻְ೘ྙͳ୉͚͘‫ؖ‬Κͮͱ͏Ζɽࢻ ְ ৚ ๅ Ͷ Γ Ε Ӏ ͘ ً ͞ ͠ Η Ζ ࢡ ੐ ੏ ‫ ޜ‬ͺ ɼ ࢻ ְ ༢ ಍ ੓ ࢡ ੐ ร Կ (Visual evokedpostural responses : VEPRs)ͳ‫ͻݼ‬ΗΖɽ઎ߨ‫Ͳڂݜ‬ͺɼVEPRs Ν଎ఈͤΖ͞ͳͲྡ৖
‫͕״‬Γ;ӫ଀਴͏͹ʹͬΔ͹඲ՃͶ΍༽͏ΔΗͱ͏Ζ[15]-[18]ɽΉͪɼӫ଀͹ଐౕΏ઴‫ͳܢ‬ഐ‫ܢ‬͹‫ܐؖ‬੓ɼबวࢻͳ஦ৼࢻ͹‫ܐؖ‬੓͵ʹ͹ߴ໪Ͷͯ͏ͱ‫ݩࣰৄݗ‬Νߨͮͪ઎ߨ
‫Ͳڂݜ‬ͺɼࣙ‫ހ‬ӣಊ͹๏޴Ώࢻ೟๏๑Ͷ‫ؖ‬ΚΔͥɼഐ‫ܻ࢙ܢ‬ͶΓΕ VEPRs ͺ൅‫ͤݳ‬Ζͳ
݃࿨෉͜ΔΗͱ͏Ζ[19]-[21]ɽ͖͢͢ɼVEPRs ͹൅ਫ਼ϟΩωθϞͺ෈໎ྐ͵఼͗ଡ͚ɼ
‫ݳ‬ে͹մ໎Ͷͺࢺͮͱ͏͵͏ɽ͠ΔͶɼVEPRs ͺࢻְ৚ๅͶًҾͤΖࢡ੐รԿͲ͍Ζ͗ɼࢻְ৚ๅΝӣಊ‫ఽ΃ׯح‬ୣͤΖࡏ͹ɼఽୣ‫ౕک‬Ͷͯ͏ͱ৆ࡋͶ‫ڂݜ‬Νߨͮͪྭͺ‫ݡ‬౲ͪΔ͵͏ɽͨ͹ͪΌɼࢻְ৚ๅͳࢡ੐੏‫ޜ‬͹ఽୣ‫ౕ͗ک‬ɼҾࢢͶΓͮͱʹ͹Γ͑ͶรԿͤ
Ζ͖Ν‫ݗ‬౾ͤΖ͞ͳ͗‫غ‬ଶ͠Ηͱ͏Ζɽରฑߩ‫ܧ‬Ͷ‫ͱؖ͢‬ɼ‫ܙ‬͹Ռָ͖Δ͹Πϕϫʖοͺɼ৿͢͏Ն೵੓Ν΍ͮͱ͏Ζɽ͞ΗΉͲ͹ͳ͞Θɼಊ༵ਦͺٌ੽ௗΏใཙ໚੷ͳ͏ͮͪ‫ݸ‬ఈద͵ਦ‫ܙ‬Ϗνʖϱ͹մੵ͕Γ;߶ଐϓʖϨΦร‫׷‬ͶΓΖबഀ਼մੵͶΓͮͱ෾ੵ͠Ηͱ͕Ε [22][23]ɼୱ९͵ϔϧΤϱ
ӣಊͳ͢ͱ‫ى‬फ़͠ΗΖ͞ͳ͗ଡ͏[24]ɽ෵ࡸ͵ਦ‫ܙ‬ϏνʖϱΝ༙͢ɼ৚ๅྖ͗୉͘͏͞
ͳ͗‫غ‬ଶ͠ΗΖൕ໚ɼಊ༵ਦ͹ΊͲ͹մੵͲͺɼฑߩ‫ؽ‬೵͹඲ՃͶͺ‫ݸ‬ֆ͍͗Ζɽͨ͞Ͳɼରฑߩ͹ฯ࣍Ͷ॑གྷ͵ࢻતٌ੽Ϗνʖϱ(ਦ 1)Νಊ༵Ϗνʖϱ(ਦ 2)ͳলΔ͢߻Κͦͱ඲ՃͤΖ͞ͳͶΓΕɼΌΉ͏ʀฑߩ‫ؽ‬೵্֒͹‫ࠬݗ‬ɼϨύϑϨτʖεϥϱҫָ͵ʹଡ෾໼Ͷ͕͏ͱ‫ر‬༫ͤΖ͞ͳ͗‫غ‬ଶ͠ΗΖɽΉͪɼາͫմ໎͠Ηͱ͏͵͏਴͏͹඲ՃͶ΍
Ԣ༽Ͳ͘Ζ͵ʹɼରฑߩ‫ܧ‬Ͷ‫ͤؖ‬Ζ‫ڂݜ‬͹൅ఴͶͺɼ‫ܙ‬͹Ռָ͖Δ͹Πϕϫʖο͗॑གྷ
Ͳ͍Ζɽͨ͞Ͳຌ‫Ͳڂݜ‬ͺɼࢻְ೘ྙͳड़ྙͳ͢ͱ͹ࢡ੐ң࣍੏‫ޜ‬͹‫ܐؖ‬Ͷ஥໪͢ɼཱི
ରӫ଀ࢻ೟࣎͹ࢻતӣಊͳ॑ৼಊ༵Νಋ࣎‫ܯ‬଎ͤΖ͞ͳͲɼࣰ‫ڧ؂ݩ‬Ͷғଚ͢͵͏ӫ଀਴͏͹඲Ճ๑Ν఑ҌͤΖͳͳ΍Ͷɼӫ଀਴͏͹൅ਫ਼‫ؽ‬঄Νմ໎ͤΖ͞ͳΝ໪దͳͤΖɽਦ 1ʁཱིରӫ଀ࢻ೟࣎Ͷ͕͜Ζࢻતٌ੽Ϗνʖϱ͹ྭɼ (a) बวࢻ೟ɼ(b) ௧ॊࢻ೟t 102 tਦ 2ʁཱིରӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵Ϗνʖϱ͹ྭɼ (a) बวࢻ೟ɼ(b) ௧ॊࢻ೟2. ࣰ‫ݩ‬2.1. ࣰ‫ݩ‬๏๑අ‫ंݩ‬ͺɼࣘʀਈ‫ع׳࣮ܧܨ‬ԡྼ͹͵͏ऑ೧஋ঃ 11 ໌(ฑ‫ۋ‬೧ྺʸඬ६ยࠫ:22.7 ʸ 0.8ࡂ)Νଲেͳ͢ͱ‫ܯ‬଎Νߨͮͪɽඅ‫ंݩ‬Ͷͺࣆ઴Ͷࣰ‫ݩ‬͹ઈ໎Νॉ෾Ͷߨͮͪ৏Ͳɼॽ໚
ͶͱಋқΝಚͪɽΉͪɼຌ‫ڂݜ‬ͺɼෳҬ୉ָ୉ָӅ޽ָ‫ڂݜ‬Ռஎ೵εητϞ޽ָ઒ߊਕ
ΝଲেͳͤΖ‫ྛڂݜ‬ཀྵҗҽճ͹ট೟Νण͜ͱࣰࢬͪ͢(ট೟൬ߺʁH2019003)ɽ
ຌ‫Ͳڂݜ‬ͺɼඅ‫͖ंݩ‬Δ 2 m ઴๏Ͳ໪͹߶͠͹Ғ஖͗஦ৼͶ͵ΖΓ͑Ͷઅ஖͠Ηͪ 55
΢ϱο͹ 3D υΡηϕϪ΢ 55UF8500(LG)Ͷӫ଀Νනࣖͪ͢ɽࣰ‫ݩ‬Ͷ༽͏Ζཱིରӫ଀ͺɼ
Sky Crystal(ΨϨϱϏηϟϠϨʖϭʖέη)Ν΍ͳͶಋऀ͹‫ڒ‬ՆΝಚͱ࠸ߑ੔ͪ͢΍͹Ν༽͏ͪ(ਦ 3)ɽSky Crystal ͺɼ‫ځ‬ରΝఆࣖͤΖಊժͲ͍Εɼࠪӊ͕Γ;৏ԾͶรҒΝ൒͏͵͗Δ 5 භब‫ۛͲغ‬ҒͳԗҒΝ६ब‫غ‬దͶԡ෰ͤΖɽ఑ࣖͪ͢ӫ଀͹‫ځ‬ର͹γ΢θͺɼۛ๏࣎͗ 9.4 [deg]ɼԗ๏࣎͗ 0.3 [deg]Ͳ͍Ζɽ‫ځ‬ରΝԗҒͳۛҒ͹ؔͲ‫׊‬Δ͖Ͷӣಊͦ͠ͱఆࣖͤΖ͞ͳͶΓΕɼ໡༹ର‫۔‬͹৵क़ӣಊΝͦ͠ͱɼ‫ء‬ൾ࿓Ν؉࿪ͤΖଠɼՀ੓ۛ
ࢻͶଲ͢ͱҲఈ͹ްՎ͍͗Ζɽຌ‫Ͳڂݜ‬ͺɼӫ଀͹ཱིର੓ 2D/3D ͗ҡ͵Ζӫ଀ΝɼͨΗͩΗबวࢻ೟Ήͪͺ௧ॊࢻ೟ͦͪ͠ɽबวࢻ೟࣎Ͳͺɼඅ‫ंݩ‬Ͷͺଲে෼Ν஭ࢻͦͥɼ
ժ໚સରΝ்ΌΖΓ͑ࢨࣖͪ͢ɽΉͪɼ௧ॊࢻ೟࣎Ͳͺɼඅ‫ंݩ‬Ͷͺଲে෼Ν஭ࢻͤΖ
Γ͑ࢨࣖͪ͢ɽ‫ܯ‬଎ͺҋ࣪Ͳߨ͏ɼࣰ‫ࢡݩ‬੐ͺཱིҒϫϱϗϩήࢡ੐ͳͪ͢ɽ॑ৼಊ༵‫ܯ‬଎Ͷͺώϧϱη Wii Ϛʖχ(Nintendo)Ν༽͏ɼӫ଀ࢻ೟࣎͹֦γϱϕϨϱή࣎ؔͲ͹॑ৼ͹Ғ஖Ν‫ى‬࿧ͪ͢ɽγϱϕϨϱήबഀ਼ͺɼ100 Hz Ͳ‫ܯ‬଎ͪ͢ɽࢻતӣಊ‫ܯ‬଎Ͷͺࢻ໼Ωϟϧ͗खΕ෉͜ΔΗͪΠ΢ϜʖέϪαʖξ EMR-9ʤψρέ΢ϟʖζτέόϫζʖʥΝ༽͏ɼӫ଀ࢻ೟࣎͹֦γϱϕϨϱή࣎ؔͲ͹ࢻત͹Ғ஖Ν‫ى‬࿧ͪ͢ɽγϱϕϨϱήबഀ਼ͺɼ60 Hz Ͳ‫ܯ‬଎ͪ͢ɽ‫ܯ‬଎஦ɼඅ‫ंݩ‬ͶͺཱིҒϫϱϗϩήࢡ੐ΝͳΔͦͪɽཱིҒ҈੫͹‫ޛ‬ɼ৏फ़͹ӫ଀ΝͨΗͩΗबวࢻΉͪͺ௧ॊࢻͲɼ֦ 60 භؔࢻ೟ͦ͠ɼ͞͹ؔ͹॑ৼಊ༵ͳࢻતӣಊΝಋ࣎‫ܯ‬଎ͪ͢ɽࢻ೟ͤΖӫ଀ͳࢻ೟๏๑͹ॳ঄ްՎΝߡྂ͢ɼࣰ‫ݩ‬ͺ೜қ͹ॳ൬Ͳߨͮͪɽ
͵͕ɼӫ଀ࢻ೟࣎Ͷ‫͏ک‬਴͏Ν‫ͪͣ״‬৖߻ͺࣰ‫ݩ‬Ν஦ࢯͲ͘Ζ΍͹ͳͪ͢ɽΉͪɼ‫ܯ‬଎஦Ͷգౕ͹΀Δͯ͘Ώϫϱϗϩήࢡ੐Νฯͱ͵͚͵ͮͪ৖߻͵ʹͺࣰ‫ݩ‬ΝࢯΌɼҲఈ࣎ؔ͹‫ܞٵ‬Νͺ͠Ίɼ࠸ౕ‫ܯ‬଎Νߨͮͪɽt 103 tਦ 3ʁࣰ‫ͪ͢༽࢘Ͳݩ‬ӫ଀

2.2. ఽୣ‫਼ؖ‬մੵӫ଀ࢻ೟࣎͹֦γϱϕϨϱή࣎ؔͲ͹ɼࢻતӣಊͳ॑ৼಊ༵͹ x - y ࠴ඬΝ‫ى‬࿧ͪ͢ɽ
ಚΔΗͪࢻતӣಊ͹υʖνͺɼx ๏޴ʤӊ๏޴Νਜ਼ʥɼy ๏޴ʤ৏๏޴Νਜ਼ʥͳͤΖࢻતҒ஖͹࣎‫ܧ‬྽Ͷร‫͢׷‬ɼ॑ৼಊ༵͹υʖνͺ x ๏޴ʤӊ๏޴Νਜ਼ʥɼy ๏޴ʤ઴๏޴Ν
ਜ਼ʥͳͤΖ॑ৼҒ஖͹࣎‫ܧ‬྽Ͷร‫ͪ͢׷‬ɽ͠ΔͶɼࢻતӣಊͳ॑ৼಊ༵͹֦੔෾͹࣎‫ܧ‬྽Ͷͯ͏ͱηϘέφϩմੵΝߨͮͪɽ͞ΗΔ͹έϫηηϘέφϩΝ‫ٽ‬Όͪ৏ͲɼࢻતӣಊΝ೘ྙɼ॑ৼಊ༵Νड़ྙͳͪ͢ਫ਼ରεητϞΝՀఈ͢ͱɼఽୣ‫਼ؖ‬մੵͶΓΕαϐʖϪϱηͳΰ΢ϱΝࢋड़ͪ͢ɽαϐʖϪϱη ‫݄݋ܥ‬ሺ݂ሻͺҐԾ͹Γ͑Ͷఈٝͪ͢ɽ
ଶห୶୷ ሺ݂ሻห
‫݄݋ܥ‬ሺ݂ሻ ൌ‫ܥ‬௫௫ ሺ݂ሻ‫ܥ‬௬௬ ሺ݂ሻሺ1ሻ͞͞Ͳɼ୶୷ ሺ݂ሻͺɼࢻતӣಊͳ॑ৼಊ༵͹৶ߺؔ͹έϫηηϘέφϩɼ‫ܥ‬௫௫ ሺ݂ሻͺɼࢻતӣಊ͹ϏϭʖηϘέφϩɼ ‫ܥ‬௬௬ ሺ݂ሻͺɼ॑ৼಊ༵͹ϏϭʖηϘέφϩͲ͍ΖɽαϐʖϪϱηͺɼ౲֚बഀ਼ଵͶ͕͏ͱɼ஍͗ 1 ͶۛͰ͚ͶͯΗࢻતӣಊͳ॑ৼಊ༵͹‫͗ܐؖ‬Ҳ࣏‫ؖ‬਼ద͵߶͏‫ؖ‬࿊੓Ν࣍ͯ‫ܐؖ‬ͶۛͰ͚͞ͳΝқັͤΖɽΉͪɼαϐʖϪϱη͹஍͗̎ͶۛͰ͚͞ͳͺɼ඲Ճ͹৏Ͳͺɼఁ͏‫ؖ‬࿊੓Νࢨͤ͞ͳͶ͵Ζɽচɼຌ‫Ͳڂݜ‬ͺ૮‫਼ܐؖ‬‫ݗ‬ఈන(r න)Ͷ‫͘Ͱخ‬ɼ‫݄݋ܥ‬ሺ݂ሻ ൐ ͲǤͲ͸ ͹৖߻ͶɼྈंͶ‫ؖ‬࿊੓͗ଚࡑͤΖͳΊ͵͢ɼͨ͹ࡏͶఽୣ‫਼ؖ‬ΰ΢ϱ͹඲ՃΝߨͮͪɽҲ๏ɼࢻતӣಊͳ॑ৼಊ༵͹ఽୣ‫਼ؖ‬ΰ΢ϱ ‫݊݅ܽܩ‬ሺ݂ሻͺɼ࣏͹Γ͑Ͷఈٝͪ͢ɽ
‫݊݅ܽܩ‬ሺ݂ሻ ൌ୶୷ ሺ݂ሻ
‫ܥ‬௫௫ ሺ݂ሻ2͞͞Ͳɼ୶୷ ሺ݂ሻͺɼࢻતӣಊͳ॑ৼಊ༵͹৶ߺؔ͹έϫηηϘέφϩɼ‫ܥ‬௫௫ ሺ݂ሻͺɼࢻતӣಊ͹ϏϭʖηϘέφϩͲ͍Ζɽఽୣ‫਼ؖ‬ͺɼࢻતӣಊΝ೘ྙɼ॑ৼಊ༵Νड़ྙͳߡ͓ͪ৖߻͹౲֚बഀ਼ଵ͹৾෱‫ܐؖ‬ΝࣖͤմੵͲ͍Ζɽΰ΢ϱͺɼ஍͗߶͏Άʹɼรಊ೘ྙͶଲ͢ɼรಊ
ड़ྙ͗୉͘͏͞ͳΝқັͤΖɽΉͪɼΰ΢ϱ͹஍Ͷͯ͏ͱɼ฾ฑ‫ۋ‬Ͷࠫ͗͵͏͞ͳΝ‫ؾ‬ໃՀ
ઈͳͤΖ :LOFR[RQ ͹ෘߺॳҒ࿪‫ݗ‬ఈΝ༽͏ͱർֳ‫ݗ‬౾Νߨͮͪɽচɼຌ‫Ͳڂݜ‬ͺ༙қਭ६Ν
S ͳͪ͢ɽt 104 t3. ݃Վ
3.1. αϐʖϪϱη
2D ӫ଀ɼ3D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹αϐʖϪϱηΝࢋड़ͪ͢(ਦ4-5)ɽ2D ӫ଀Ͳͺɼबวࢻ೟࣎͹ 0.16 Hz ෉ۛͲ૮‫͗ؖ‬ΊΔΗ͵͖ͮͪɽͨ͹ଠ͹बഀ਼ଵͲͺɼ૮‫͗ؖ‬ΊΔΗͪ(p<0.05)ͪΌɼ૮‫͗ؖ‬ΊΔΗͪଵҮΝΰ΢ϱ͹඲Ճଲেͳ͢
ͪɽΉͪɼ3D ӫ଀Ͳͺɼबวࢻ/௧ॊࢻͶ͕͏ͱɼͤ΄ͱ͹बഀ਼ଵҮͲ૮‫͗ؖ‬ΊΔΗͪ(p<0.05)ɽ3D ӫ଀ࢻ೟࣎Ͳͺɼ͏ͥΗ͹ྭͶ͕͏ͱ΍ΰ΢ϱ͹඲Ճଲেͳ͵ͮͪɽਦ 4ʁ2D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹αϐʖϪϱηɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴ਦ 5ʁ3D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ ͹αϐʖϪϱηɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴

3.2. ΰ΢ϱ
2D ӫ଀͕Γ; 3D ӫ଀ࢻ೟࣎Ͷ͕͜Ζࢻતӣಊͳ॑ৼಊ༵͹ఽୣ‫਼ؖ‬մੵ͖Δࢋड़͢
ͪΰ΢ϱΝർֳͪ͢(ਦ 6-9)ɽӫ଀ࢻ೟࣎Ͷ͕͜Ζ x ࣢๏޴͹ർֳͲͺɼࢻ೟๏๑ؔͲ༙қࠫͺΊΔΗ͵͖ͮͪɽ2D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ y ࣢๏޴͹ർֳͲͺ௧ॊࢻͶർ΄ɼबวࢻͲ 0.2-0.4 Hz ෉ۛ͹ΰ΢ϱ༙͗қͶଁ୉ͪ͢(p<0.05)ɽҲ๏ɼ3D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ y ࣢๏޴͹ർֳͲͺ௧ॊࢻͶർ΄ɼबวࢻͲ 0.15-0.2 Hz ෉ۛ͹ΰ΢ϱ༙͗қͶଁ୉ͪ͢(p<0.05)ɽ

t 105 tਦ 6ʁ2D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹ఽୣ‫਼ؖ‬մੵ͖Δࢋड़ͪ͢ΰ΢ϱ͹ࢻ೟๏๑ؔർֳɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴ਦ 7ʁ3D ӫ଀ࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹ఽୣ‫਼ؖ‬մੵ͖Δࢋड़ͪ͢ΰ΢ϱ͹ࢻ೟๏๑ؔർֳɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴࣏Ͷɼࢻ೟๏๑͟ͳͶ෾͜ͱӫ଀ؔർֳΝߨͮͪɽx ࣢๏޴͹ർֳͶ͕͏ͱ 2D ӫ଀बวࢻ೟࣎Ͷർ΄ɼ3D ӫ଀बวࢻ೟࣎͹ 0.1-0.2 Hz ෉ۛ͹ΰ΢ϱ༙͗қͶଁ୉ͤΖܑ޴͗ΊΔΗͪ(p<0.10)ɽΉͪɼबวࢻ೟࣎Ͷ͕͜Ζ y ࣢๏޴͹ർֳͲͺɼӫ଀ؔͲ༙қ͵ࠫͺΊΔΗ͵͖ͮͪɽҲ๏ɼ௧ॊࢻ೟࣎Ͳͺ x ࣢๏޴ɼy ࣢๏޴ͳ΍Ͷɼӫ଀ؔͲ༙қ͵ࠫͺΊΔΗ͵͖ͮͪɽਦ 8ʁबวࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹ఽୣ‫਼ؖ‬մੵ͖Δࢋड़ͪ͢ΰ΢ϱ͹ӫ଀ؔർֳɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴

t 106 tਦ 9ʁ௧ॊࢻ೟࣎Ͷ͕͜Ζ॑ৼಊ༵ͳࢻતӣಊ͹ఽୣ‫਼ؖ‬մੵ͖Δࢋड़ͪ͢ΰ΢ϱ͹ӫ଀ؔർֳɼ(a) x ࣢๏޴ɼ(b) y ࣢๏޴

4. ߡࡱຌ‫Ͳڂݜ‬ͺɼཱིରӫ଀ࢻ೟࣎Ͷ͕͜Ζࢻતӣಊͳ॑ৼಊ༵Νಋ࣎‫ܯ‬଎͢ɼࢻְͳࢡ੐
ң࣍੏‫ޜ‬͹‫ܐؖ‬੓Ν໎Δ͖ͳͤΖ͞ͳͲɼӫ଀਴͏͹‫ؽ‬঄͹৆ࡋΝմ໎ͤΖ͞ͳΝ໪దͳ͢ɼࣰ‫ݩ‬Νߨͮͪɽͨ͹݃Վɼྈӫ଀ࢻ೟࣎ͳ΍Ͷ y ࣢๏޴Ͷ͕͏ͱɼ௧ॊࢻͶർ΄बวࢻ͹ΰ΢ϱ͗ଁ୉ͤΖ͞ͳ͗ࣖ͠Ηͪ(ਦ 6bɼ7b)ɽ͞Ηͺबวࢻ࣎Ͷ͕͏ͱɼࢻત
ӣಊ(೘ྙ)͹ଁ୉ͶଲͤΖ॑ৼಊ༵(ड़ྙ)͹ଁ୉͹ౕ߻͏͗୉͘͏͞ͳΝࣖ͢ͱ͏Ζɽࢻְ৚ๅͺɼ୉೶ൿ࣯Ώ஦೶͵ʹ͹஦਽ਈ‫Ͳܧܨ‬౹߻ʀॴཀྵ͠Ηɼରฑߩ΃ͳఽୣ͠
ΗΖͪΌɼबวࢻͲͺ೶Ͳ͹գ৔͵ॴཀྵً͗͘ͱ͏ΖՆ೵੓͗ࣖࠨ͠ΗΖɽ͞Η͗೶͹ෝ୴ͳ͵Εɼରฑߩ΃͹৚ๅॴཀྵʀఽୣ͗෈ॉ෾ͳ͵Ζɽͨ͹ͪΌɼӫ଀਴͏ΝӀً͘͢͞Ώͤ͏ͳߡ͓ΔΗΖɽҲ๏ɼࢻ೟๏๑ͶғଚͦͥͶഐ‫ܢ‬ӫ଀ͺ࣎ؔรԿ͢ͱ͏ΖͪΌɼVEPRs ͺ൅‫͏ͱ͢ݳ‬Ζ΍͹ͳߡ͓ΔΗΖɽ͖͢͢ɼຌ‫ڂݜ‬͹ఽୣ‫਼ؖ‬մੵ͹݃ՎɼबวࢻͶർ΄௧ॊࢻ͹ΰ΢ϱ͗ཊ੏͠ΗΖՆ೵੓͗ࣖࠨ͠Ηͪ(ਦ̖ɼ9)ɽ͞Ηͺɼ௧ॊࢻͶ൒͏஦ৼࢻְ࿑͹৚ๅॴཀྵ͗༑ҒͶ͵Εɼഐ‫ܢ‬ӫ଀͹೟எ͗๨͝ΔΗͱɼVEPRs ͗ཊ੏͠Ηͪͳਬࡱ͠ΗΖɽӫ଀ؔ͹ർֳΝߨͮͪͳ͞Θɼ௧ॊࢻͲͺཱིର੓͹ҩ͏ͶΓΔͥɼΰ΢ϱ͹ଁ෱ً͗͞Δ͵͖ͮͪ(ਦ 9)ɽ௧ॊࢻͺबวࢻͳҡ͵Εɼ‫ځ‬ରΝࢻતͶ௧ॊͦ͠Ζࢻ೟๏๑Ͳ͍Εɼ‫ځ‬ର͗ࢻඬͳ͵Ζ͞ͳͲɼࢻְ৚ๅ͖ΔԘ௜๏޴Ώਭฑ๏޴͹घ͖͗ΕΝಚΖ͞ͳ͗Ն೵ͳ͵Ζɽ͞ΗͶΓΕɼϐφ͗ࢡ੐Νฯ࣍ͤΖͪΌͶචགྷ͵ࢡ੐ൕࣻ͗ਜ਼৙ͶߨΚΗͱ͏ΖɽαϐʖϪϱηմੵ͹݃Վ͖Δɼ0.15-0.4 Hz ͹बഀ਼Ͳͺɼࢻְ͗৚ๅΝण͜खΖ
ͳࢡ੐੏‫ߨ͗ޜ‬ΚΗΖ͞ͳ͗ߡ͓ΔΗΖ͗ɼࢡ੐ൕࣻ͹գఖͲͺɼࢻતӣಊͳ॑ৼಊ༵
͹৾෱͗ಋఖౕͲ͍ΖͪΌɼΰ΢ϱ͹ଁ෱ً͗͞Δ͵͖ͮͪɽΉͪɼबวࢻ ࣎Ͳͺɼ2Dӫ଀Ͷർ΄ 3D ӫ଀͹ΰ΢ϱ͹஍͗ଁ୉ͤΖ͞ͳ͗ࣖ͠Ηͪ(ਦ 8)ɽ॑ৼಊ༵‫ࠬݗ‬ͺɼӫ଀਴͏͹඲Ճ๑ͳ͢ͱ༽͏ΔΗͱ͕Εɼӫ଀਴͏൅঳࣎ɼಊ༵ྖ͗ଁ୉ͤΖ͞ͳ͗எΔ
Ηͱ͏Ζ[25]ɽ৏फ़ͪ͢ΰ΢ϱ͹ଁ୉ͺɼಊ༵ྖ͹ଁ୉Νࣖ͢ͱ͕Εɼ3D ӫ଀ࢻ೟࣎Ͷΰ΢ϱ͹஍༙͗қͶଁ୉ͤΖܑ޴͗ΊΔΗͪͳ͏͑͞ͳͺɼ3D ӫ଀ͶΓͮͱӫ଀਴͏͗Ӏً͘͞͠Ηͪͳ͏͓Ζɽͨ͹ͪΌɼΰ΢ϱ͹ଁ෱ི͗߶͏͞ͳͶΓΕɼ਴͏‫ͨ;ٶ‬͹ౕ߻͏Ν඲ՃͤΖ͞ͳ͗Ͳ͘ΖɽҲ๏ɼӫ଀͹ཱིର੓ͶғଚͦͥͶഐ‫ܢ‬ӫ଀ͺ࣎ؔรԿt 107 t͢ͱ͏ΖͪΌɼVEPRs ͺ൅‫͏ͱ͢ݳ‬Ζ΍͹ͳߡ͓ΔΗΖɽ͖͢͢ɼ3D ӫ଀ͺԠߨ͘৚ๅΝ༙͢ͱ͕Εɼഐ‫ܢ‬ӫ଀͖Δ‫ؔۯ‬೟எΝึؔͤΖްՎ͍͗ΖɽΓͮͱɼ3D ӫ଀ࢻ೟࣎Ͷ͕͏ͱ VEPRs ͗‫͚ک‬൅‫͢ݳ‬ɼಊ༵ྖ͗ଁ୉ͪ͢ͳਬࡱ͠ΗΖ(ਦ 8)ɽ
࢝ͯ͹‫ܯ‬଎Ϗνʖϱ͹͑ͬɼ3D/बวࢻ࣎Ͷ࠹΍ΰ΢ϱ͹ଁ෱ི͗߶͏͞ͳ͗ࣖ͠Η
ͪɽ3D/बวࢻ͹ૌΊ߻Κͦͺӫ଀਴͏ΝӀً͘͢͞Ώͤ͏͞ͳ͗எΔΗͱ͕Ε [7][26]ɼ
ӫ଀਴͏൅঳࣎Ͷΰ΢ϱ͗ଁ୉ͤΖ΍͹ͳߡ͓ΔΗΖɽΉͪɼ৏फ़͹Γ͑Ͷ VEPRs Ν‫ک‬͚൅‫ͦ͠ݳ‬ΖૌΊ߻ΚͦͲ͍ΖͳਬࡱͲ͘ΖɽVEPRs ͗ɼࢻְͳฑߩ‫ְ״‬͹‫෈ְ״‬Ҳ஗Ν༩๹ͤΖ໪దͲ൅‫͏ͱ͢ݳ‬Ζͳߡ͓Ζͳɼΰ΢ϱ͹ଁ୉ͺ໅८ΝմভͤΖͪΌ͹ࣙӶൕԢͫͳߡ͓Ζ͞ͳ͗Ͳ͘Ζɽͨ͹ͪΌɼࢻતӣಊͳ॑ৼಊ༵ΝͨΗͩΗ೘ड़ྙͳͪ͢
ͳ͘͹ఽୣ‫਼ؖ‬մੵͶΓΖΰ΢ϱ͹ࢋड़͗ɼӫ଀਴͏͹৿ͪ͵඲Ճ๑ͳ͵ΖՆ೵੓͗ࣖࠨ͠Ηͪɽӫ଀͹ཱིର੓ͶғଚͦͥͶɼबวࢻ࣎Ͷ 0.15-0.4 Hz ͹बഀ਼ଵͶ͕͜Ζΰ΢ϱ͗ଁ୉ ͢ ͪ ( ਦ 6b ɼ 7b) ɽ ৼ ധ ร ಊ մ ੵ Ͷ ͕ ͏ ͱ ͺ ɼ ‫ ٷ ݼ‬ब ‫ غ‬͹ ร ಊ Ν න ͤ ߶ ब ഀ ੔ ෾
ʤ0.15-0.40 HzʁHFʥͳ݄ѻรಊΝൕӫͤΖఁबഀ੔෾ʤ0.04-0.15 HzʁLFʥͶϒʖέ͗‫ݳ‬Ηɼ͞͹ྈंͺཱࣙਈ‫׈ܨ‬ಊΝൕӫͤΖͳ͠ΗΖ[27]ɽಝͶɼHF ͺ෯ި‫״‬ਈ‫׈ܨ‬ಊΝɼLF ͺި‫״‬ਈ‫׈ܨ‬ಊͳ෯ި‫״‬ਈ‫׈ܨ‬ಊ͹ྈंͶғଚͤΖɽ͵͕ɼ઴ఋ‫ཱࣙͳܧ‬ਈ‫ܧܨ‬ͺɼմ๦ָదͶ΍ు‫ـ‬ਫ਼ཀྵָదͶ΍ືં͵‫͍͗ܐؖ‬Ζ͞ͳ͗எΔΗͱ͏Ζ [28][29]ɽΉͪɼࢻְ‫ཱࣙͳܧ‬ਈ‫ܧܨ‬ͺືંͲ͍Εɼ͞Ηͺ಑޺͗෯ި‫״‬ਈ‫״ިͳܨ‬ਈ‫ܨ‬͹ 2 ॑ࢩഓΝण͜ͱ͏Ζ͞ͳ͖Δ໎Δ͖Ͳ͍Ζɽबวࢻ͹৖߻ɼHF ੔෾͹बഀ਼ଵͶ͕͜Ζΰ΢ϱ͗ଁ୉͢ͱ͕Ε(ਦ 6bɼ7b)ɼ෯ި‫״‬ਈ‫׈ܨ‬ಊ΍ΰ΢ϱͳ࿊ಊ͢ͱထ਒͢ͱ͏Ζ͞ͳ͗͑
͖͓͗ΖɽΉͪɼ3D ӫ଀͹बวࢻ೟࣎Ͳͺɼ0.1-0.2 Hz ͹ LF ੔෾ͳ HF ੔෾͹बഀ਼ଵͶΉͪ͗ͮͱɼΰ΢ϱ͗ଁ୉ͤΖ͞ͳ͗ࣖ͠Ηͪ(ਦ 8)ɽ෯ި‫״‬ਈ‫״ިͳܨ‬ਈ‫׈ܨ‬ಊΝൕӫͤΖ LF ͗ଁ୉ͪ͢͹ͺ 3D ӫ଀ࢻ೟࣎͹ΊͲ͍Εɼ2D ӫ଀ࢻ೟࣎ͲͺΊΔΗ͵͖ͮͪɽҐ৏ΓΕɼ3D ӫ଀ࢻ೟࣎Ͷ͕͏ͱɼ2D ӫ଀ࢻ೟࣎ΓΕ΍ި‫״‬ਈ‫׈ܨ‬ಊ͗ထ਒ͤ
Ζ͞ͳͲɼ಑޺͗֋ࢆ͢ɼඅࣺֆ਄ౕ͗ఁԾͤΖ͞ͳͶΓΕӫ଀Ϛί͗ਫ਼ͣͱɼΰ΢ϱ͹ଁ୉Ώӫ଀਴͏Ͷͯ͵͗Ζ͞ͳ͗ߡ͓ΔΗΖɽ

5. ΉͳΌ
ຌ‫Ͳڂݜ‬ͺɼࢻְ೘ྙͳड़ྙͳ͢ͱ͹ࢡ੐ң࣍੏‫ޜ‬͹‫ܐؖ‬Ͷ஥໪͢ɼཱིରӫ଀ࢻ೟࣎͹ࢻતӣಊͳ॑ৼಊ༵Νಋ࣎‫ܯ‬଎ͤΖ͞ͳͲɼӫ଀਴͏͹‫ؽ‬঄͹৆ࡋΝմ໎ͤΖ͞ͳΝ໪దͳ͢ɼࣰ‫ݩ‬Νߨͮͪɽͨ͹݃Վɼࢻતӣಊͳ॑ৼಊ༵Ν೘ड़ྙͳͪ͢ΰ΢ϱ͹஍ͺɼӫ଀ؔ͹ҩ͏͍Ζ͏ͺɼࢻ೟๏๑ؔ͹ҩ͏ͶΓΕรԿ͗ΊΔΗͪɽαϐʖϪϱηմੵ͹݃Վ͖Δɼ3D ӫ଀ࢻ೟࣎Ͳͺɼ͏ͥΗ͹ྭͶ͕͏ͱ΍ΰ΢ϱ͹඲Ճଲেͳ͵ͮͪɽ࣏Ͷɼఽୣ‫਼ؖ‬մੵ͹݃Վ͖Δɼ2D ӫ଀Ͷർ΄ 3D ӫ଀ࢻ೟࣎Ͷΰ΢ϱ͗ଁ୉ͤΖ͞ͳ͗ࣖ͠ΗͪɽΉͪɼ௧ॊࢻͶർ΄बวࢻ͹ΰ΢ϱ͗ଁ୉ͤΖ͞ͳ͗ࣖ͠Ηͪɽबวࢻ͹৖߻ɼHF ੔෾͹बഀ਼ଵͶ͕͜Ζΰ΢ϱ͗ଁ୉͢ͱ͕Εɼ෯ި‫״‬ਈ‫ܨ‬‫׈‬ಊ΍ΰ΢ϱͳ࿊ಊ͢ͱထ਒͢ͱ͏Ζ͞ͳ͖͓͗͑͗Ζɽ3D/बวࢻ͹ૌΊ߻Κͦͺɼӫ଀਴͏ΝӀً͘͢͞Ώͤ͏͞ͳ͗எΔΗͱ͕Εɼӫ଀਴͏൅঳࣎Ͷΰ΢ϱ͗ଁ୉ͤΖ΍͹ͳਬࡱ͠ΗΖɽຌ‫Ͳڂݜ‬ͺɼVEPRs ͹൅‫ͳݳ‬ΰ΢ϱ͹ଁ୉Ͷͺ‫ؖ‬࿊͍͗Ζ͞ͳ͗ࣖࠨ͠Ηͪɽࢻְͳฑߩ‫ְ״‬͹‫෈ְ״‬Ҳ஗ͶଲͤΖਐରద‫͏߶ౕ͗״‬৖߻Ͷ VEPRs ͗‫͚ک‬t 108 t൅‫ͤݳ‬Ζͳߡ͓Ζͳɼΰ΢ϱ͹ଁ୉ͺ໅८ΝմভͤΖͪΌ͹ࣙӶൕԢͲ͍Εɼΰ΢ϱΝ
඲ՃͤΖ͞ͳͲ਴͏͹ఖౕΝ൓இͲ͘Ζͳਬࡱ͠ΗΖɽःࣛຌ‫ڂݜ‬ͺɼཱི੶Ռָٗ ढ़৾‫ࡔڷ‬஄ ‫ঁڂݜ‬੔(A)ɼ‫ਁל‬৚ๅՌָ৾‫ ࡔڷ‬஄ ‫ঁڂݜ‬੔ɼ
JSPS Ռ‫ݜ‬ඇ 18K11417, 20K12528 ͹ঁ੔Νणͪ͜΍͹Ͳͤɽࢂߡช‫ݛ‬[1]ੋ‫࡜ރ‬ఱ෋, ਁీ༠ղ, ஝ీ‫ھ‬nωʖθ௒ࠬͶ‫ͪ͏Ͱخ‬ଡࢻ఼‫ ܗ‬VR ‫ࡒگ‬͹֋൅ͳद‫ۂ‬
ࣰભ| ೖຌώʖοϡϩϨΠϨτΡָճ࿨ชࢿ , 11(4), pp.537-543, 2006.

[2]‫ٳ‬ฯీવඛ, ࢃԾ५, Ԡଞ৶ଢ ࿢ ଠ nଢཇ‫ܧ‬εϝϣϪʖεϥϱΝཤ༽݆ͪ͢͹ຮָͬܿ͜स͹ࣰભͳްՎ| Ռָ‫گ‬ү‫ڂݜ‬, 31(4), pp.248-256, 2007.

[3]ᖝ‫ޔ؝‬࿢ , n3D υΡηϕϪ΢Ͷ͕͜Ζਕؔ޽ָద඲Ճͳඬ६Կ |, ӫ଀৚ๅϟυΡΠָճٗढ़ๅࠄ, 33(16), pp.9-12, 2009.

[4]‫ޛ‬౽ྲࢢ, ޽౽ദহ, ࠦ౽ߠฑ ଠ nࣙ‫ހ‬ӣಊ‫ְ״‬Ν༢಍ͤΖࢻְ࢙ܻͶଲͤΖਫ਼ରൕԢ͹෾ੵ| ӫ଀৚ๅϟυΡΠָճ, 60, pp.589-596, 2006.

[5]໼ଞ‫ܛ‬ཀྵ, ໨ཿబ, ൩ౣ५ඛ ଠ, nਫ਼ର৶ߺ͖Δਬఈͪ͢ӫ଀਴͏ͳͨ͹͖ͮ͘͜ͳ͵ͮͪӫ଀͹ಊ͘ϗέφϩ͹ಝ௅ | ుࢢ৚ๅ௪৶ָճ, 89, pp.576-583, 2006.

[6]ྵ໨५Ҳ, নຌ‫ڦ‬, ಛଁ޲್ ଠn॑ৼಊ༵‫ࠬݗ‬͹ Q&A घӀ͘|(TXLOLEULXPResearch,
55(1), pp.64-77, 1996.

[7]

M. Takada, Y. Fukui, Y. Matsuura et al., n3HULSKHUDO YLHZLQJ GXULQJ H[SRVXUH WR D
2D/3D video clip effects on the human body|, Environ Health Prev. Med., 20(2),pp.79-89, 2015.

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[12] $6(GZDUGVn%RG\VZD\DQGYLVLRQ|-([S3V\FKRO , 36, pp.526-535, 1946.
[13] :0 3DXOXV $ 6WUDXEH 7 %UDQGW n9LVXDO VWDELOL]DWLRQ RI posture. Physiological
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[14] H.C. Diener, J. Dichgans, M. Bacher et al.n4XDQWLILFDWLRQRISRVWXUDOVZD\LQQRUPDOV

t 109 t

DQG SDWLHQWV ZLWK FHUHEHOODU GLVHDVHV| (OHFWURHQFHSKDORJU. Clin. Neurophysiol., 57,
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[15] M. Ohmi, nSensation of self-motion induced by real-world stimuli|, Proc. Int. Work.
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[16] J. Freeman, S.E. Avons, R. Meddis et al., nUsing Behavioral Realism to Estimate
3UHVHQFH $ 6WXG\ RI WKH 8WLOLW\ RI 3RVWXUDO 5HVSRQVHV WR 0RWLRQ 6WLPXOL| 3UHVHQFH
Teleoperators and Virtual Environments, 9, pp.149-164, 2000.
[17] /-6PDUW7$6WRIIUHJHQ%*%DUG\n9LVXDOO\LQGXFHGPRWLRQVLFNQHVVSUHG icted by
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[18] S.J. Villard, M.B. Flanagan, G.M. Albanese et al., n3RVWXUDO LQVWDELOLW\ DQG PRWLRQVLFNQHVVLQDYLUWXDOPRYLQJURRP|+XP)DFWRUV ., 50, pp.332-345, 2008.
[19] .+ %ULWWHQ n0HFhanisms of self-PRWLRQ SHUFHSWLRQ| $QQX. Rev. Neurosci, 31,
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[29] &' %DODEDQ - '3RVWHU n1HXURDQDWRPLF VXEVWUDWHV IRU YHVWLEXORDXWRQRPLF
LQWHUDFWLRQV|-9HVWLEXODU5HVHDUFKSS-16, 1998.

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(2021 ೧ 2 ݆ 1 ೖण෉ɾ2021 ೧ 2 ݆ 1 ೖणཀྵ)1. ͺͣΌͶ
λʖεϡϩυΡηνϱηͶͯ͏ͱߡࡱ͢Γ͑ɽαϫψՔ͹Ծɼಝް༂Ώϭέοϱ͗Ҳൢ͹ਕʓͶ෕‫͏͵͏ͱ͢ٶ‬য়‫Ͳڱ‬ɼͳΕ͑Ζ༙ް͵કྲྀͺɼλʖεϡϩυΡηνϱηΝฯͯ
͞ͳͲ͍Ζɽͨ͞Ͳɼ͍Ζ෨ԲͶλʖεϡϩυΡηνϱηΝฯͬ͵͗ΔՁਕ͗೘Ζ͞ͳ͗
Ͳ͘Ζ͖Νߡ͓Γ͑ʤਦ̏ࢂলʥɽ͠ΔͶୱ९ԿͤΖͳɼҲఈ͹྘ҮͶλʖεϡϩυΡην
ϱηΝฯͬ͵͗ΔɼՁਕ͗೘ΗΖ͖Νߡ͓Ζ͞ͳͶ͵Ζɽ͞͞ͲͺɼPython Ν࢘ͮͱ Lʹ
L ͹ਜ਼๏‫ܙ‬͹ϚρέηͶɼ‫͏ޕ‬Ͷ࠹ఁ r ͹‫཯ړ‬Νฯͬ͵͗ΔՁ‫ݺ‬͹఼Νഓ஖Ͳ͘Ζ͖Νߡ͓Γ͑ɽ

ਦ 1ʁҲఈ྘Үʤྭ͓ͻ෨ԲʥͶλʖεϡϩυΡηνϱηΝฯͬ͵͗Δਕ͗͏Ζ༹ࢢɽ

t 111 tλʖεϡϩυΡηνϱηΝฯͮͱ͏Ζ༹ࢢΝ໎ࣖͤΖͪΌɼਦ 1 Ͷ௜‫ ܚ‬r ͹ԃ൭Νॽ͘Յ͓ͪ΍͹͗ਦ 2 Ͳ͍Ζɽਦ 2 Ν‫ݡ‬ΖͳɼλʖεϡϩυΡηνϱηฯͬ͵͗ΔਕΝഓ஖ͤΖ໲ୌͺɼԃ൭͹ϧϱξϞϏρΫϱή͹໲ୌͶ‫ؾ‬஥͠ΗΖ͞ͳ͗෾͖Ζɽ໲ୌ͗੖ཀྵͲ͘
ͪ͹ͲɼPython Ν࢘ͮͱϧϱξϞϏρΫϱή͹εϝϣϪʖεϥϱࣰ‫ݩ‬Ν͢ͱΊΓ͑ɽ͵͕ɼPyrhon ͹ϕϫήϧϝϱή‫ͱ͢ͳڧ؂‬ͺɼGoogle Colaboratory[1]Ν࢘͑ɽ࣏Ͷɼήϧϓࡠ੔͵ʹඵժ͹࢕๏Ͷͯ͏ͱफ़΄ΖɽPython ͹ඵժͲͺɼtkinter ͗Γ͚࢘ΚΗΖ͗ɼColaboratory ͺ tkinter Νγϛʖφ͢ͱ͏͵͏ɽͨΗΑ͓୊ 1 յߪ࠴Ͳͺɼ
Turtle Graphic Ν࢘ͮͱɼಊద͵εϝϣϪʖεϥϱ͹නࣖΝࢾΊͪɽࠕյͺɼεϝϣϪʖεϥϱ͹݃ՎΝήϧϓ͵ʹͲ෾͖ΕΏ͚ͤනࣖͤΖ Python ͹ϧ΢ϔϧϨ matplotlib [2]Ν়ղͤΖɽmatplotlib ͺɼtkinter ͳർ΄Ζͳࣙ༟͵ඵժͺ੏‫͠ݸ‬ΗΖ͗ɼήϧϓ͵ʹΝ؈ୱͶࡠΗΖϟϨρφ͍͗Ζɽ͵͕ɼColaboratory ͹ϙʖϞϘʖζͶΠέιηͤΖͳड़ͱ͚
ΖʰColaboratory ΃Γ͑ͨ͞ʱͶ͕͏ͱ΍ɼυʖν͹ՆࢻԿ͹๏๑ͳ͢ͱ matplotlib ়͗ղ͠Ηͱ͏Ζɽrਦ 2ʁ‫ ཯ړ‬r ͹λʖεϡϩυΡηνϱηΝฯͮͱ͏Ζ༹ࢢΝࣖͤͪΌਕΝ஦ৼͶ௜‫̓ܚ‬͹ԃ൭Νඵ͘ଏͪ͢΍͹ɽ

2. 3\WKRQ ͲϧϱξϞϏρΫϱή
2.1. &RODERUDWRU\ Ͳ 3\WKRQ ϕϫήϧϝϱή
୊̏յߪٝͲɼColaboratory Ν࢘͑ͳ؈ୱͶ Python ϕϫήϧϝϱή͗Ͳ͘Ζ͹Ν়ղͪ͢ɽ͞͞ͲɼColaboratory ͶΓΖ Python ͹ϕϫήϧϝϱή‫ڧ؂‬Ͷͯ͏ͱɼ୊ 1 յߪٝ[3]Ν؈݁Ͷ৾ΕศΘ͑ɽWeb ৏͹ Colaboratory ͶΠέιη༹ͪ͢ࢢͳɼαʖχιϩ΃͹
ϕϫήϧϞ͹೘ྙ૤ࡠ͹༹ࢢΝਦ 3 Ͷࣖͤʤ୊ 1 յߪٝ͹ਦΝඵ͘‫͓ͪ׷‬΍͹ʥɽαʖχιϩͶ Python ͹αʖχΝ೘ྙͲ͘ΖΓ͑ͶͤΖͳɼ६ඍͺश྅ɼ‫ޛ‬ͺϕϫήϧϝϱήͲ
͍ΖɽColaboratory ͹ཤ༽ͶͺɼGoogle ͹ΠΩΤϱφ͗චགྷ͵͹Ͳɼ࣍ͮͱ͵͏ਕͺΠΩΤϱφΝखಚ͢Γ͑ɽ͵͕ɼColaboratory Ͳ͵͚ͱ΍ Python ͗ૺΖ idle ͵ʹ͹‫Ͳڧ؂‬΍
ྒྷ͏[4]ɽ

t 112 ta)b)ԾͶαʖχιϩΝૢ೘ʤέϨρέͤΖʥ৿͢͏αʖχιϩ͗ࡠΔΗͪ

ਦ 3ʁGoogle Colaboratory ΃͹Πέιηɽa)ʰColaboratory ΃Γ͑ͨ͞ʱ͹ Web Ϙʖζɼb)ϕϫήϧϞ͹೘ྙ͹ͪΌ͹αʖχιϩ͹ਫ਼੔ɽ਩͘ड़͢(ၠၡ )Ͳαʖχιϩ Νૢ೘ͤΖ༹ࢢΝઈ໎͢ͱ͏ΖɽતͲҕΉΗͱ͏Ζ෨෾͗૤ࡠͳ Colaboratory ͹ಊࡠͲ͍Ζɽ

t 113 t2.2. PDWSORWOLE Ν࢘͑؈ୱͶήϧϓΝࡠ੔Ͳ͘Ζ Python ϧ΢ϔϧϨ matplotlib Ν࢘ͮͱɼ‫و‬ଉద͵఼͹ഓ஖ɼϧϱξϞ͵ഓ஖ɼλʖεϡϩυΡηνϱηΝߡྂͪ͢ϧϱξϞ͵ഓ஖ʷԃ൭͹ϧϱξϞϏ
ρΫϱήʷɼΝࡠժ͢ͱ͏͑͞ɽ

2.2.1. つ๎ⓗ࡞Ⅼࡢ㓄⨨λʖεϡϩυΡηνϱη r Νߡྂ͢͵͗Δɼ/ʹ/ ͹ਜ਼๏‫྘ܙ‬ҮͲ͹ਕ͹ഓ஖Νߡ͓ͱΊΓ͑ɽୱ९Կ͹ͪΌਕ͹୉͘͠ΝໃࢻͲ͘ΖͳͤΖͳɼਕΝ఼ͳΊ͵ͦΖɽ͞͹ୱ९Կͺɼ༙‫྘ݸ‬ҮͲ͹ഓ஖Νߡ͓ͪ৖߻ɼ‫ڧ‬ֆͲ͹ഓ஖΍؈ୱԿ͢ͱ͚ΗΖɽ఼ͺ୉͘͠Ν࣍ͪ͵͏͹Ͳɼ‫ڧ‬ֆત৏Ͷഓ஖Ͳ͘ΖΓ͑Ͷ͵Ζɽ͞͞Ͳɼγ΢θ༙͗‫͍Ͳݸ‬Ζԃ൭͹ϧϱξϞ
ϏρΫϱήͳ͏͑ࢻ఼͖Δߡ͓ͱΊΓ͑ɽͤΖͳɼ/ʹ/ ͹ਜ਼๏‫྘ܙ‬ҮͲ͹‫ ཯ړ‬r Νฯ఼ͮͪ͹ഓ஖ͺɼ(Lʶr)ʹ(Lʶr)͹ਜ਼๏‫྘ܙ‬Ү΃͹௜‫ ܚ‬r ͹ԃ൭͹ϏρΫϱήͳ౵Ճ͵໲ୌͶ‫ؾ‬஥͠ΗΖɽϧϱξϞ͵ഓ஖Νߡ͓Ζ઴Ͷɼ‫و‬ଉద͵ഓ஖Νߡࡱ͢ͱ͕͑͞ɽ۫ରద͵ྭͳ͢ͱͺɼָߏ͹‫࣪گ‬͹࠴ੰ͹ഓ஖ɼߪಌʤϙʖϩʥ͹ࣞఱͲ͹ด;͵ʹΝࢧ͏ූ͖΄ͱΊΓ͑ɽ͞͹Γ͑͵৖߻ɼୱ९ԿͤΖͳਜ਼๏֪ࢢ৏΃͹఼͹ഓ஖Ͷ͵Ζɽ͠ͱɼmatplotlib Ν࢘ͮͱɼ఼͹ഓ஖͹ਦΝࡠΘ͑ɽ̓ʻ̣/10 ͳͤΖͳɼਜ਼๏֪ࢢ৏΃͹‫و‬ଉద͵఼͹ഓ஖͹ͳ͘ɼ11ʹ11=121 ‫ݺ‬͹఼Νഓ஖Ͳ͘Ζɽࡠਦ͹ͪΌ͹ϕϫήϧϞͺɼmatplotlib ͹ϙʖϞϘʖζͶ͍ΖγϱϕϩϕϫήϧϞΝࢂߡͶͪ͢ɽਦ 4 ͺɼਜ਼๏֪ࢢ৏΃͹఼͹ഓ஖ϏνʖϱΝɼ
matplotlib Ν࢘ͮͪ Python ϕϫήϧϞʤϕϫήϧϞϨηφ̏ʥͲ੏ࡠͪ͢΍͹Ͳ͍ Ζɽࠕյ࢘ͮͪ Python ͹ໍྫ͹ΉͳΌ̏ɿimport ชͶΓΖϧ΢ϔϧϨ͹ಣΊࠒΊ̐ɿfor ชΝ࢘ͮͪϩʖϕ̑ɿif ชΝ࢘ͮͪ෾‫ز‬̒ɿdef ชͶΓΖ‫਼ؖ‬͹ఈٝ
Python ͹ϕϫήϧϝϱήͶͯ͏ͱͺɼࢂߡช‫[ݛ‬4][5]ΝࢂߡͶ͢ͱ͚ͫ͠͏ɽ
ʴ‫ۯ‬പͳνϔ͗೘ͮͱ͏ΖͳɼΦϧʖͶ͵Ζͳ͍͗͘Ζ͹ͲαϟϱφͶͺ஭қʵϕϫήϧϞϨηφ̏
import matplotlib.pyplot as plt
import numpy as np
data = np.array([[],[]])# ‫ۯ‬͹ numpy2 ࣏‫ݫ‬ഓ྽Ν६ඍfor i in range(11):for j in range(11):newdisk = np.array([[i],[j]])t 114 tdata = np.append(data,newdisk,axis=1)
fig, ax = plt.subplots(figsize=(5,5))
ax.scatter(data[0], data[1])plt.show()ϕ ϫ ή ϧ Ϟ ͹ Ϋ ʖ ϛ ΢ ϱ φ Ν մ ઈ ͢ Γ ͑ ɽ ࠹ ॵ Ͷ ɼ import Ν ࢘ ͮ ͱ ɼ ϧ ΢ ϔ ϧ Ϩmatplotlib ͳ numpy ΝಣΊࠒΊ࢘༽Ͳ͘ΖΓ͑ͶͤΖɽ࣏ͶɼϕϫρφͤΖ఼͹࠴ඬΝ
numpy ͹ 2 ࣏‫ݫ‬ഓ྽ data Ͷେ೘͢ɼmatplotlib ͹ pyplot Ν࢘ͮͱ఼͹ϕϫρφΝ͕͞͵ͮ ͱ ͏ Ζ ɽ ࠹ ‫ ޛ‬Ͷ ɼ matplotlib.pyplot.show() Ͳ ή ϧ ϓ Ν න ࣖ ͢ ͱ ͏ Ζ ɽʤ ஭ ʁ import
matplotlib.pyplot as plt ͳ ͢ ͱ ಣ Ί ࠒ Ξ Ͳ ͏ Ζ ͹ Ͳ ɼ matplotlib.pyplot.show() ˢ
plt.show()ɼ matplotlib.pyplot.subplots() ˢ plt.subplots() ͳ ঴ ྲྀ Ͳ ͘ Ζ ɽ ͵ ͕ ɼ import
matplotlib ͳ͢ͱಣΊࠒ΋ͳ঴ྲྀͲ͘͵͏͹Ͳ஭қ͢Γ͑ɽʥ

ਦ 4ʁPython ͹ϧ΢ϔϧϨ matplotlib ࢘ͮͱ੏ࡠͪ͢ਦʁਜ਼๏֪ࢢ৏Ͷ఼Νഓ஖ͪ͢΍͹ɽ

͞͞ͲɼLʹL ͹ਜ਼๏‫ܙ‬͹Ϛρέη΃ɼ௜‫̓ܚ‬͹ԃ൭͗ैలͲ͘Ζ࠹୉‫਼ݺ‬Νߡ͓ͱ͕͞
͑ɽ‫ڧ‬ֆ͗͵͏৖߻͹ฑ໚΃͹࠹ືैలͺɼࢀֱ֪ࢢ͹֪ࢢ఼৏Ͷഓ஖ͤΖ͞ͳͶଲԢͤ
Ζɽ͖͢͢ɼ‫ڧ‬ֆ͍͗Ζ༙‫ݸ‬γ΢θ͹Ϛρέη΃͹ैల͹৖߻ͺɼͤؔ͗͘Ͳ͘ͱ͢Ή͏ɼ࠹ືैలͶͺ͵Δ͵͏ɽLʹL ͹ਜ਼๏‫ܙ‬͹Ϛρέη΃ɼ̓ʻ̣/10 ͹ԃ൭ΝैలͤΖ৖߻͹࠹୉‫਼ݺ‬ͺɼ10ʹ6+9ʹ5ʻ106 ‫͵ͳݺ‬Ζɽ͖͢͢ɼปࡏͶഓ஖ͤΖ͞ͳΝ‫͏ͱ͢ڒ‬Ζ͹Ͳɼԃ൭͹ϏρΫϱήͳͺঙ͢ҡ͵Ζɽ͕‫͏ޕ‬͹‫࠹͗཯ړ‬ఁͲ΍̓཯ΗΖɼͯΉΕ࠹ۛં‫཯ړ‬͗ r Ґ৏ͳ͏͑଍ളড়݇Ͳ͹఼͹ഓ஖ͳ͵Ζɽ10̣ʙL(sin М/3)=11.547ʞΓΕɼঘ਼఼ҐԾ઀ΕࣼͱͤΖͳɼ11 ૜͹ηϘʖη͍͗Ζ͹Ͳɼྈ୼Ν೘Ηͱ 12 ૜͹఼Νഓ஖Ͳ͘ΖɽΓͮͱɼ఼͗ 12 ‫ݺ‬͹૜͗ 6 ૜ɼ10 ‫ݺ‬͹૜͗ 6 ૜ɼ‫ ܯ‬11ʹ6+10ʹ6ʻ126 ‫ݺ‬͹఼Νഓ஖Ͳ
͘Ζɽ۫ରదͶ఼Νഓ஖ͤΖ༹ࢢΝɼਦ̓Ͷࣖ͢͵͗ΔΊͱ͏͑͞ɽ࠹ॵͶɼਜ਼๏‫ܙ‬͹Ϛρέt 115 tη͹αʖψʖ΃఼Νഓ஖ͤΖʤਦ 5a)ʥɽ࣏ͶɼปʤวʥͶԌͮͱ఼Νഓ஖͢ͱ͏͚ʤਦ 5b)ʥɽ
ͨ͢ͱɼ૜Ν੷Ί॑͸ΖΓ͑Ͷഓ஖ͤΖʤਦ 5c)ʥɽ࠹‫ޛ‬Ͷɼ‫و‬ଉదͶ఼Νഓ஖ͪ͢৖߻͹
ഓ஖Ͳ͘Ζ఼͹‫਼ݺ‬ΝΉͳΌΖͳɼࢀֱ֪ࢢ৏ 126 ‫ݺ‬ɼਜ਼๏֪ࢢ৏ 121 ‫ݺ‬ɼͳ͵Ζɽ

a)

c)

b)

ਦ 5ʁਜ਼๏‫ܙ‬͹ϚρέηͶɼ‫و‬ଉద࠹ືैల͢ͱ͏༹͚ࢢɽ a) αʖψʖͶഓ஖ɼb) ปͶԌͮͱഓ஖͢ͱ͏͚ɼc) ૜(layer)Ν੷Ί॑͸Ζɽ

2.2.2. ࣛࣥࢲ࣒࡞Ⅼࡢ㓄⨨LʹL ͹ਜ਼๏‫ܙ‬͹Ϛρέη΃͹ϧϱξϞ͵఼͹ഓ஖Νߡ͓ΖɽΉͥɼλʖεϡϩυΡην
ϱηΝߡྂͦͥͶɼ100 ‫ݺ‬͹఼Νഓ஖͢ͱΊΓ͑ʤϕϫήϧϞϨηφ̐ʥɽਦ 6 ͶɼҲ༹ཛྷ਼Ν༽͏ͱɼ100 ͹఼Νഓ஖ͪ͢΍͹Νࣖͤɽಋ࣎Ͷɼ࠹ۛં‫཯ړ‬͹෾ා΍‫ٽ‬Όͪʤਦ 6͹ӊͶࣖͤʥɽਦ͖̔ΔɼλʖεϡϩυΡηνϱηΝߡྂ͢͵͏ͳɼ࠹ۛં‫཯ړ‬͹෾ා͖Δ
΍ືͶ͵Ζίʖη͗ଡ਼൅ਫ਼ͤΖ͞ͳ͗෾͖ΖɽϕϫήϧϞϨηφ̐
import matplotlib.pyplot as plt
import numpy as np
np.random.seed(20201230)# ཛྷ਼͹झ

data = np.array([[],[]])
histdistance = np.array([])# ࠹ۛં‫཯ړ‬͹Ϩηφ

ndisk = 0

# Number of disks ͹ॵ‫غ‬஍

def calnearestdistance(x, y,ndisk):mindistance = 999999# Հ͹࠹ঘ஍ʤ࠹ۛં‫཯ړ‬ʥ

for i in range(ndisk):
distance = np.sqrt((data[0,i]-x)**2 + (data[1,i]-y)**2)
if (distance != 0) & (distance < mindistance):
mindistance = distancet 116 t# distance=0(ࣙਐ)͹఼Νঈ͚

return mindistancefor i in range(100):
newdisk = np.random.rand(2,1)
data = np.append(data,newdisk,axis=1)
ndisk += 1
for i in range(ndisk):# ࠹ۛં‫཯ړ‬͹ϨηφΝࡠ੔r = calnearestdistance(data[0,i],data[1,i],ndisk)
histdistance = np.append(histdistance,np.array([r]))fig, axs = plt.subplots(1,2, figsize=(11, 5))# 1 ߨͶ 2 ͯ͹ਦaxs[0].scatter(data[0], data[1])axs[1].hist(histdistance)plt.xlabel("Distance"), plt.ylabel("Number of Persons")
plt.show()ϕ ϫ ή ϧ Ϟ Ϩ η φ 2 ͹ ಼ ༲ Ν ؈ ୱ Ͷ մ ઈ ͢ Γ ͑ ɽ numpy ϧ ΢ ϔ ϧ Ϩ ͹ ‫਼ ؖ‬
np.random.seed() Ͳ ཛྷ ਼ ͹ झ Ν ݀ Ό Ζ ɽ ࠹ ۛ ં ఼ ͳ ͹ ‫ ཯ ړ‬Ν ‫ ͤ ࢋ ܯ‬Ζ ‫ ͱ ͢ ͳ ਼ ؖ‬ɼcalnearestdistance(x, y,ndisk)ΝఈٝͤΖɽ࠴ඬ(x, y)Ν೘ྙͤΖͳ data Ͷౌ࿧͠Ηͪ ndisk‫ݺ‬͹఼͹࠴ඬ͹஦͹΍ͮͳ΍ۛં͢ͱ͏Ζ఼ͳ͹‫཯ړ‬Νศ͢ͱ͚ΗΖɽΉͪɼnumpy ͹‫ؖ‬਼ append ͲϓΟ΢ϩͶυʖνΝ෉͜Յ͓ͱ͏Ζɽ͞͹ϕϫήϧϞͲͺɼ࠹ۛં‫཯ړ‬͹෾ාΝ‫ٽ‬ΌΖͪΌͶ࢘ͮͱ͏Ζ͗ɼϧϱξϞϏρΫϱή͹εϝϣϪʖεϥϱΝ͕͞͵͑ͳ͘Ͷͺɼԃ൭͗॑͵ΔͥͶഓ஖Ͳ͘Ζ͖Ν൓இͦ͠Ζ॑གྷ͵ༀׄΝ୴͑͞ͳͶ͵Ζɽਦ 6ʁҲ༹ཛྷ਼Ν࢘ͮͱ 100 ‫ݺ‬͹఼Ν෾ාͦͪ͠΍͹ɽࠪ͗‫ؔۯ‬෾ාɼӊ͗࠹ۛં‫཯ړ‬͹෾ාɽt 117 tλʖεϡϩυΡηνϱηΝߡྂͪ͢εϝϣϪʖεϥϱΝ͕͞͵͑ɽΓΕ‫ືݭ‬Ͷ‫ͳ͑ݶ‬ɼ
LʹL ͹ਜ਼๏‫྘ܙ‬ҮͶ࠹ۛં‫̓͗཯ړ‬Ґ৏཯͢ͱ఼ΝϧϱξϞͶഓ஖ͤΖ໲ୌΝߡ͓Ζʤ (Lʶr)ʹ(Lʶr)͹ਜ਼๏‫ܙ‬͹Ϛρέη΃ɼ௜‫̓ܚ‬͹ԃ൭͹ϧϱξϞϏρΫϱήͳ౵ՃͲ͍Ζʥɽ͞͞Ͳͺɼ̓Ν̣/10 ͳ͢ͱΊΓ͑ɽλʖεϡϩυΡηνϱηΝߡྂ͢ͱɼ͕‫͏ޕ‬͹‫࠹͗཯ړ‬ఁͲ΍̓཯ΗΖΓ͑Ͷ͢ͱɼϧϱξϞϏρΫϱήΝ͕͞͵ͮͪͳ͘͹఼͹ഓ஖Νਦ 7 Ͷࣖͤɽਦ 7 ͹ӊଈ͹࠹ۛં‫཯ړ‬͹ළౕ෾ා͹ήϧϓ͖Δ΍఼֦͗࠹ఁ̓(ʻ̣/10)཯Ηͱ͏Ζ͹͗෾͖Ζɽಋ࣎ͶɼεϝϣϪʖεϥϱ݃Վ͖Δɼ΍ͮͳ΍཯Ηͱ͏Ζ΍͹Ͳ΍ 1.35̓͹‫཯ړ‬Ґ಼Ͳ͍Ζ͞ͳ͗෾͖Ζɽ

ਦ 7ʁ఼͹෾ාͳۛં‫཯ړ‬͹෾ාɽLʹL ͹ਜ਼๏‫ܙ‬͹྘ҮͶ࠹ۛં‫ ͗཯ړ‬L/10 Ґ৏Ͷ͵ΖΓ͑Ͷ‫཯ړ‬Ν཯͢ͱ෾ාͦͪ͠εϝϣϪʖεϥϱ݃Վ͹ྭɽ 100 ຬյ͹ࢾߨͲ 82 ਕΝഓ஖Ͳ͘ͱ
͏ΖɽΠϩβϨθϞʤϕϫήϧϞϨηφ 3ʥͶͯ͏ͱઈ໎͢Γ͑ɽࠕյ͹ΠϩβϨθϞͲͺɼҲ༹ཛྷ਼Ν൅ਫ਼ͦ͠ͱɼഓ஖͢Γ͑ͳ఼ͪ͢͹࠹ۛં఼ͳ͹‫཯ړ‬Ν̓ N ͳͪ͢ͳ͘ɼ̓ ̥ ʽ̓Ͷ͵ͮͪ৖߻ͺɼഓ஖ͦͥͶɼཛྷ਼Ν࠸ౕ൅ਫ਼ͦ͠ͱ͏Ζɽཛྷ਼Ν 100 ຬյ൅ਫ਼ͦ͠ͱ
‫ٽ‬Όͪ͹͗ਦ 7 Ͳ͍Ζɽཛྷ਼Ν࢘ͮͱ 100 ຬյ͹ϧϱξϞϏρΫϱήΝͦ͠Ζ͹Ͷ 526 භʤ༁ 9 ෾ʥ͖͖ͮͪɽͨ͹݃Վɼ82 ਕΝഓ஖ͤΖ͞ͳ͗Ͳͪ͘ɽ͠ΔͶɼ300 ຬյ͹ࢾߨ
ʤ1581 භʤ༁ 26 ෾ʥʥɼ500 ຬյ͹ࢾߨʤ2647 භʤ༁ 44 ෾ʥʥΝ͕͞͵ͮͱ΍ɼ82 ਕҐ৏Νഓ஖Ͳ͘͵͖ͮͪɽࢾߨ࣎ؔͺɼColaboratory Ͳࣰߨͪ͢ͳ͘͹΍͹Ͳ͍Ζɽ͵͕ɼཛྷ਼͹झΝร͓Ζͳ݃Վ͗รΚΖ͞ͳͶ஭қ͢Γ͑ɽϕϫήϧϞϨηφ 3
import mathimport matplotlib.pyplot as plt
import numpy as np
NTRIAL = 1000000# ࢾߨյ਼

np.random.seed(20201230)# ཛྷ਼͹झ

data = np.random.rand(2,1)# ࠹ॵ͹ਕ͹Ғ஖

histdistance = np.array([])# ࠹ۛં‫཯ړ‬͹Ϩηφt 118 tsocialdistance = 0.1# Social Distancendisk = 1

# Number of disks ͹ॵ‫غ‬஍

def calnearestdistance(x, y,ndisk):mindistance = 999999# Հ͹࠹ঘ஍ʤ࠹ۛં‫཯ړ‬ʥ

for i in range(ndisk):
distance = math.sqrt((data[0,i]-x)**2 + (data[1,i]-y)**2)
if (distance != 0) & (distance < mindistance):# distance=0(ࣙਐ)Νঈ֐ͤΖ

mindistance = distance
return mindistancefor i in range(NTRIAL):
newdisk = np.random.rand(2,1)
r = calnearestdistance(newdisk[0],newdisk[1],ndisk)
if r >= socialdistance:data = np.append(data,newdisk,axis=1)
ndisk += 1
for i in range(ndisk):# ࠹ۛં‫཯ړ‬͹ϨηφΝࡠ੔r = calnearestdistance(data[0,i],data[1,i],ndisk)
histdistance = np.append(histdistance,np.array([r]))print('Number of disks is ',ndisk)
fig, axs = plt.subplots(1,2, figsize=(11, 5))# 1 ߨͶ 2 ͯ͹ਦaxs[0].scatter(data[0], data[1])axs[1].hist(histdistance)plt.xlabel("Distance"), plt.ylabel("Number of Persons")
plt.show()ϕϫήϧϞϨηφ 3 ͹ึଏઈ໎Ν͢Γ͑ɽϕϫήϧϞϨηφ 2 Ͳ΍࢘ͮͪɼ࠴ඬ(x, y)Ν೘ྙ͢ɼdata Ͷౌ࿧͠Η఼ͪ‫ͳ܊‬͹࠹ۛં‫཯ړ‬Νศͤ‫ ਼ؖ‬calnearestdistance(x, y,ndisk)͗Ϋʖϛ΢ϱφͲ͍Ζɽ఼͹ഓ஖͕͗͞͵ΚΗΖգఖΝΊΖͪΌͶɼεϝϣϪʖεϥϱ౏஦͹఼͹ഓ஖Νਦ 8 Ͷࣖͤɽ͞͞ͲͺɼΦϪΪϱφͲްིద͵ΠϩβϨθϞͶͺɼ఼॑Ν͕͏ͱ͏͵͏ɽ఼Ν஖͚৖ॶΝཛྷ਼Ν൅ਫ਼ͦ͠ͱ݀Όͱ͏Ζ͹Ͳɼ‫ع‬Ͷഓ஖͠Η఼ͪ͹‫਼͗ݺ‬ଡ͚͵ΖͶͪ͗͢͏φϧ΢ΠϱχΦϧʖ͗ଡ͚͵Ζɽ࠹ॵ͹఼͹ഓ஖ͺɼ‫ ཯ړ‬r Ґ಼Ͷଠ͹఼͹ഓ஖͗͵͏͹Ͳɼφϧ΢ΠϱχΦϧʖ͹චགྷͺ͵͏ɽ͖͢͢ɼ2 ൬໪Ґ߳͹఼͹ഓ஖ͺ࠹ۛં‫͗཯ړ‬̓ҐԾͶ͵ͮͪ৖߻ɼഓ஖͢௜͠͵͜Ηͻ͵Δ͵͏ɽཛྷ਼Ν൅ਫ਼ͦͪ͠յ਼ͺɼ 5 ‫ݺ‬͹ഓ஖Ͷͺ 5 յɼ10 ‫ݺ‬͹ഓ஖Ͷͺ 11 յɼ20 ‫ݺ‬͹ഓ஖Ͷͺ 25 յɼ40 ‫ݺ‬͹ഓ஖Ͷͺ 95 յɼ80‫ݺ‬͹ഓ஖Ͷͺ 51240 յɼͨ͢ͱ࠹‫ޛ‬͹ 82 ‫ݺ‬͹ഓ஖Ͷͺ 121970 յɼ͹ࢾߨ͗චགྷͲ͍ͮ

t 119 tͪɽਦ 9 Ͷɼࢾߨյ਼ vs.ഓ஖Ͷ੔ޯ఼ͪ͢͹‫਼ݺ‬͹ϕϫρφΝࣖͤɽ఼ΝϧϱξϞͶഓ஖ͪ࣎͢͹ഓ஖ްིͶͯ͏ͱߡ͓ͱΊΖɽ࠹ۛં‫̓཯ړ‬Νң࣍͢͵͗
Δ LʹL ͹ਜ਼๏‫ܙ‬͹྘ҮͶഓ஖Ͳ͘Ζ఼͹࠹୉‫਼ݺ‬ͺɼ126 ‫͍Ͳݺ‬ΖɽϧϱξϞ͵఼͹ഓ஖εϝϣϪʖεϥϱͲͺ 82 ‫ݺ‬͹఼Νഓ஖ͤΖ͞ͳ͗Ͳͪ͘͹Ͳɼ82/126˼0.65ɼ୉ࡸ೼Ͷ 2/3 ͹ްིͲ఼͗ഓ஖Ͳͪ͘͞ͳ͗෾͖ͮͪɽ͖͢͢ɼ໎Δ͖Ͷ 82 ͳ͏͑‫਼ݺ‬ͺઊଲͲͺ͵͏ɽཛྷ਼͹झΝร͓ͪεϝϣϪʖεϥϱΝ͕͞͵͑͞ͳͶΓͮͱɼഓ஖Ͳ͘Ζ఼͹‫਼͗ݺ‬รΚΖɽྭ͓ͻɼϕϫήϧϞϨηφ 3 ͹ 5 ߨ໪͹ཛྷ਼͹झΝร͓ͱɼnp.random.seed(20210110)ͳͤΖͳɼഓ஖Ͳ͘Ζ఼͹‫਼ݺ‬ͺ 77 Ͷ͵Ζɽ‫خͪ͢ࡎܟ‬ຌͳ͵ΖϕϫήϧϞʤϕϫήϧϞϨηφ 3ʥΝཤ༽ͤΖͳɼཛྷ਼͹झΝร͓Ζ͵ʹ͠Ή͡Ή͵͞ͳ͗ࢾͦΖɽ͠ΔͶɼ਼ߨ͹αϜϱχΝ௧ՅͤΖͫ͜ͲɼՆ೵੓͗߁
͗Ζɽྭ͓ͻɼϚρέηͳԃ൭̓͹ർΝ 10:1 Ͷͪ͢΍͹ΝΊͱͪ͗͘ɼ͞͹ർΝร͓ͱΊ
Ζͳʹ͑รΚΖ͖΍໚പ͏τʖϜͲ͍Ζɽͧͽɼಣं͹๏ʓ͗͏Θ͏Θࢾ͢ͱ͚ͫ͠Ηͻ
߀͏Ͳ͍ΖɽϕϫήϧϞΝร͓ͱ͏͚͑ͬͶɼPython ͹ϕϫήϧϝϱήͶ΍‫׵‬Ηͱ͏͚͞ͳ͗‫غ‬ଶ͠ΗΖ͹Ͳɼ͏Θ͏Θͳࢾ͢ͱֺ͢ΞͲΆ͢͏ɽ
Python ͹ϧ΢ϔϧϨ matplotlib Ν࢘͑͞ͳͶΓΕɼ؈ୱͶήϧϓΝࡠΗΖ͞ͳ͗Ͳ͘Ζ͹ΝΊͱͪ͘ɽ͞͹Γ͑Ͷɼϧ΢ϔϧϨ͗ैࣰ͢ͱ͏Ζ͹͗ Python ͹ಝ௅͹ͽͳͯͲ͍Ζɽสཤ͵ϧ΢ϔϧϨΝ‫ͯ͜ݡ‬Ζ͹΍ Python ϕϫήϧϝϱή͹ֺ͢ΊͲ͍ΖɽPython ͺɼָ;Ώͤ͏ϕϫήϧϝϱή‫͍Ͳޢݶ‬Εʤ[4]Νࢂলʥɼ͠ΔͶ Colaboratory Ν࢘͑ͳͤ͛Ͷ࢟ΌΔΗΖɽͧͽɼηϜʖφϓΧϱ͵ʹͲֺ͢ΞͲ௘ͪ͜Δࢧ͑ɽΉͪɼϕϫήϧϞͺ‫ܙ‬͹Ռָճ͹ HP ͖Δ download Ͳ͘ΖΓ͑ͶͤΖ༩ఈͲ͍Ζɽ
ʴʤ஭ʥColaboratory ͹ Home Page[1]͖ΔΫϡϕοϡʖͪ͢ਦ 3 ͺɼຌཔΩϧʖͲ͍ΕപࠉͲһࡰͤΖͳ‫ݡ‬Ͷ͚͏৖߻͍͗ΕΉͤɽʵt 120 tਦ 8ʁϧϱξϞϏρΫϱή͹༹ࢢɽ 5 ‫ݺ‬ɼ10 ‫ݺ‬ɼ20 ‫ݺ‬ɼ40 ‫ݺ‬ɼͨ͢ͱ࠹शয়ସ(82 ‫ࣖ͗͠)ݺ‬Ηͱ͏Ζɽt 121 tਦ 9ʁࢾߨյ਼ vs.ਕ਼͹ϕϫρφɽःࣛ‫ߚݬ‬ΝಣΞͲ༙ӻ͵αϟϱφΝ͢ͱ͚ͫͮͪ͠∃ీभध‫گ‬दɼ୉ָӅਫ਼͹߶௣࿪‫܇ن‬ΝͺͣΌͳͤΖෳҬ୉ָ୉ָӅ޽ָ‫ڂݜ‬Ռஎ೵εητϞ޽ָ઒ߊඉત‫ܙ‬Ռָ‫࣪ڂݜ‬͹ϟϱώʖͶ‫״‬ः͏ͪ͢Ήͤɽࢂߡช‫ݛ‬[1]

Google Colaboratory

https://colab.research.google.com/notebooks/intro.ipynb#[2]

matplotlib.org[3]ฑీཾ߀ʁColaboratory Ͳ‫ܙ‬͹ՌָΝֺ͢΍͑ʷαρϙ‫ۄ‬ત Νඵ͏ͱΊΓ͑ʷ ɼ‫ܙ‬͹Ռ

https://matplotlib.org

ָճࢿɼ35 ‫ת‬ɼ1 ߺɼ75-80ɼʤ2020ʥ[4]

ฑ ీ ཾ ߀ ʁ Python Ν ࢟ Ό ͱ ̏ 0 ೖ Ͳ ΰ ʖ Ϟ Ν ࡠ Η Ζ Γ ͑ Ͷ ͵ Ζ ͹ ͖ ʷ ̔ ̏ ࡂ ͖ Δ ͹ ேકʁ͖̎Δ࢟ΌΖ Python Programmingʷɾ‫ܙ‬͹Ռָճࢿɼ35 ‫ת‬ɼ1 ߺɼ55-74ɼ
ʤ2020ʥ

[5]έζϧඊߨ‫ط‬ʁκϫ͖ΔΏ͚͢͠ͺͣΌΖ Python ೘໵ɼϜ΢ψϑड़൝ɼpp.255ɼʤ2018ʥ

ߪ࠴Ͷ‫͠ࡎܟ‬ΗͪϕϫήϧϞͺɼ‫ܙ‬͹Ռָճ͹ HP ͹ҐԾ͖ΔξΤϱϫʖχͲ͘Ήͤɽ
https://katachi-jp.com/journal35ΩρφˏϘʖηφͲ Colaboratory ͹αʖχιϩͶహΕ෉͜ͱɼૺΔͦͱΊͱ͚ͫ͠͏ɽ

t 122 t