\mathrm{m}_{\text{ }}$ ( ) 1. :? $\dagger_{\vee}\mathrm{a}$ (Escherichia $(E.)$ co $l\mathrm{i}$) (Bacillus $(B.)$ subtilis) $0\mu

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1 \mathrm{m}_{\text{ }}$ ( ) 1. :? $\dagger_{\vee}\mathrm{a}$ (Escherichia $(E.)$ co $l\mathrm{i}$) (Bacillus $(B.)$ subtilis) $0\mu 05\sim 1 $2\sim 4\mu \mathrm{m}$ \nearrow $\mathrm{a}$ 1

2 88 2) 3). 2. $(B$. subfilis) (B. naito) OG-OI ( ). 9cm $\mathrm{t}\mathrm{v}$ $\mathrm{t}\mathrm{v}$

3 87 l/(conc. of Agar) $[1f(\mathrm{g}/l)]$ 1: ( 5cm ) (3 $\mathrm{m}\mathrm{m}$ ) 2 $C_{a}$ ( ) $C_{n}$ $35^{\text{ }}\mathrm{c}$ $C_{n}$ ) C 1 A

$$\mathrm{a}$ $\mathrm{b}$ 88 $\mathrm{d}\mathrm{l}$ 2: A A 2 172 $\mathrm{d}\mathrm{l}$ A ( ) 13-16) 2 $\mathrm{d}\mathrm{l}$ A$

4 $\mathrm{a}$ $\mathrm{b}$ 88 $\mathrm{d}\mathrm{l}$ 2: A A $\mathrm{d}\mathrm{l}$ A ( ) 13-16) 2 $\mathrm{d}\mathrm{l}$ A $\mathrm{d}\mathrm{l}$ A A 17) $\mathrm{d}\mathrm{l}$ 18) A $C_{a}$ $C_{n}$ $\mathrm{b}$ 3(a) Eden 19,20) ( 3(b) ) $1_{\sqrt}\mathrm{a}_{\mathrm{O}}$

5 89 (a) (b) $\mathrm{b}$ 3: (a) (b)

6 $\mathrm{e}$ $\mathrm{e}$ $\mathrm{d}_{\text{ }}$ 90 $\mathrm{d}$ 4: 7 Eden 19-21) $\alpha$ ( ) 078 Eden 05 87, $\mathrm{b}$ Eden $\mathrm{c}_{\text{ }}\mathrm{d}_{\text{ }}$ C 1 A $\mathrm{b}$ $\mathrm{c}_{\text{ }}$ 1 $\mathrm{a}_{\text{ }}$ $\mathrm{b}$ $\mathrm{d}$ 4 1 D 7)

7 $\mathrm{d}$ 97 $\mathrm{d}$ A $\mathrm{e}$ BM $\langle$ (dense-branching morphology) 5 (a) $\mathrm{d}$ $\mathrm{d}\mathrm{l}$ BM A 14-16,22) 5(b) $\mathrm{d}$ $3$ 2 $\text{ }$ $\mathrm{c}$ 11,12,23) 6 ( ) 2 $\text{ }$ $3$ $\text{ }4$ 3 $\mathrm{c}$ 12) (1) $\rangle$ (2 2 quorum ( ) sensing ) 34)

8 92 (a) (b) $\mathrm{e}$ $\mathrm{d}\mathrm{b}$ 5: (a) M (b)

9 93 $\mathrm{c}$ 6: ( Proteus $Proteus\rangle\text{ }$ 24-26) mirabilis ( $Se\tau\cdot rat\mathrm{i}amarcescens^{\backslash )}$ 1 A $\mathrm{e}$ $\mathrm{b}$ A $\mathrm{e}$ A 5cm $\mathrm{b}$ A 1 4, 5 $\mathrm{d}$ 1 $\mathrm{c}$ $\mathrm{e}$ A $\mathrm{b}$ $\mathrm{c}_{\text{ }}\mathrm{e}$ A $\mathrm{d}\mathrm{l}$ A $\mathrm{d}$ $\}_{\sqrt}\mathrm{a}$ 1

10 94 $Vg(B)$ $D_{b}$ 7: A $\mathrm{b}$ $\mathrm{c}_{\text{ }}\mathrm{d}_{\text{ }}\mathrm{e}$ 5) 4.. $N(r, t)$ 7

11 $\mathrm{t}_{l}\mathrm{a}$ 95 8: $B(r, t)$ ; $\frac{\partial B}{\partial t}=\nabla(d_{b}\nabla B)+\nu g(b_{\grave{j}}n)b$ (1) $D_{b}$ 1 2 $\nu$ $g(b, N)$ $D_{b}$ 28) $g(b, N)=1-B/K$ (1) $\frac{\partial B}{\partial t}=d_{b}\nabla^{2}b+l/b(1-\frac{b}{k})$ (2) $\mathrm{d}$ $K$ 28) 7) ) 30) $D_{b}=DNB$

12 $\frac{\partial B}{\partial t}$ $\frac{\partial N}{\partial t}$ $\frac{\partial B_{a}}{\partial t}$ $\frac{\partial N}{\partial t,}$ $=\nabla^{2}n-nb_{a}$ 96 9: $D=d\{1+\omega(r)\}$ ( $d$ ) $\iota/=1_{\text{ }}g(b, n)=n$ $\omega(r)$ $ \omega <1$ $=$ $d\nabla\cdot\{(1+\omega)nb\nabla B\}+NB$, (3) $=$ $\nabla^{2}n-nb$ (4) $d$ $n_{0}$ A $\mathrm{e}_{\text{ }}\mathrm{d}$ $\mathrm{c}$ $\mathrm{e}$ ) ( 5(b) ) $B(r, t)$ 32) $B_{a}(r, t)$ $B_{i}(r, t)$ $B=B_{a}+B_{i}$ 9 : $=$ $d\nabla^{2}b_{a}+\epsilon NB_{a}-a(B_{a}, N)B_{a}$, (5), (6)

13 $\frac{\partial B_{i}}{\partial t}$ 97 $d$ 10:. $=$ $a(b_{a}, N)B_{a}$. (7) 1 ( 1 ) $a(b_{a}, N)$ 1 3 $\alpha(b_{a_{?}}n)$ $N$ $a(b_{a}, N)$ B $a(b_{a}, N)$ $a(b_{a}, N)=a_{0}(1+N)^{-1}(1[perp], B_{a})^{-1}$ 32). 10 $\mathrm{c}$ 32) 1 10 no $d$ $C_{n}$ $C_{a}^{-1}$ ( 1)

14 Hout B $\mathrm{b}$ $\mathrm{b}$ 10 1 ( 3(b) ) 3 Db=dlB (5) 1 $n_{0}$ $d_{1}$ A $\mathrm{b}_{\text{ }}\mathrm{d}$ 33) Db=d0+dlB $d_{1}$ $n_{0}$ $d_{0}$ 33) 5 $\mathrm{b}$ $\mathrm{c}$ $\mathrm{c}$ 1 $\mathrm{c}$ $\mathrm{c}$ $ (2$. 1 : $\mathrm{o}$ ( ) 1) P. Ball: Critical Mass - One Thing Leals to Another -, (Farrar, Straus and Giroux, New York, 2004). 2) P. Singleton: Introluction to Bacteria, 2nd ed (Wiley, New York, i992). 3) J. A. Shapiro and M. Dworkin (ed.): Bacteria as Multicellular Orgamisms (Oxford Univ. Press, New York, 1997).

15 99 4) H. Fujikawa and M. Matsushita: J. Phys. Soc. Jpn. 58 (1989) ) M. Ohgiwari, M. Matsushita and T. Matsuyama: J. Phys. Soc. Jpn, 61 (1992) ) : ( ) 64 (1994) ) J. Wakita, K. Komatsu, A. Nakahara, T. Matsuyama and M. Matsushita: J. Phys. Soc. Jpn. 63 (i994) ) J. Wakita, H. Itoh, T. Matsuyama and M. Matsushita: J. Phys. Soc Jpn. 66 (1997) 67. 9) M. Matsushita: in Ref 3), pp ) J. Wakita, I. Rafols, H. Itoh, T. Matsuyama and M. Matsushita: J. Phys. Soc. Jpn. 67 (1998) ) J. Wakita, H. Shimada, H. Itoh, T. Matsuyama and M. Matsushita: J. Phys. Soc. Jpn. 70 (2001) ) H. Shimada, T. Ikeda, J. Wakita, H. Itoh, S. Kurosu, F. Hiramatsu, M. Nakatsuchi, Y. Yamazaki, T. Matsuyam a and M. Matsushita: J. Phys. Soc. Jpn. 73 (2004) ) T. A Witten and $\mathrm{i}_{\lrcorner}$. M. Sander; Phys. Rev, Lett. 47 (1981) ) D. Avnir (ed.): The Fractal Approach to Heterogeneous Chemistry, (Wiley, Chichester, 1989), 15) T. Vicsek: Fractal Growth Phenomena, 2nd Ed. (World Scientific, Singapore, 1992) ; T. : ( 1990). 16) P. Meakin: Fractals, Scaling and Growth Far From Equilibrium, (Cambridge University Press, $\mathrm{c}\mathrm{a}\mathrm{m}\mathrm{b}\mathrm{r}\mathrm{i}\mathrm{d}\mathrm{g}\mathrm{e},1998$ ). 17) M. Matsushita and H. Fujikawa: Physica A 168 (1991) ) T. Matsuyama and M. Matsushita: Appl. Environ. Microbiol. 58 (1992) 1227; $C.R$. C. Crit. Rev. Microbiol. 19 (1993) ) F. Family and T. Vicsek (cd): Dynamics of Fractaf Surfaces, (World Scientific, Singapore, 1991). 20) A. -L. Barabasi and H. E. Stanley: Fractal Concepts in Surface Growth, (Cambridge University Press, Cambridge, 1995). 21) : ( ) 66 (1996) 184.

16 Yamazaki Matsushita: ) E. Ben-Jacob and P. Garik: Nature 343 (1990) ) H. Fujikawa: Physica A 189 (1992) ) A. Nakahara, Y. Shim $\mathrm{a}\mathrm{d}\mathrm{a}$ Soc. Jpn. 65 (1996) 2700., J. Wakita, M. Matsushita and T. Matsuyama: J. Phys. 25) O. Rauprich, M. Matsushita, C. J. Weijer, F. Siegert, S. E. Esipov and J. A. Shapiro: J. Bacteriol. 178 (1996) $6\acute{0}25$. 26) H. Itoh, J. Wakita, T. Matsuyar a and M. Matsushita: J. Phys. Soc. $\mathrm{j}\mathrm{p}\mathrm{n}$ $68(1999)$ 27) T. Matsuyama, Y. Takagi, Y. Nakagawa, H. Itoh, J. Wakita and M. Matsushita: J. Bacteriol 182 (2000) ) J. D. Murray: Mathematical Biology (Springer-Verlag, Berlin, 1989). 29) E. Ben-Jacob, 0. Shochet, A. Tenenbaum, I. Cohen, A. Czirok and T. Vicsek: Nature 368 (1994) ) K. Kawasaki, A. Mochizuki, M. Matsushita, T. Um eda and N. Shigesada: $\mathrm{j}$ Biol. 188 (1997) ) S. Kitsunezaki: J. Phys. Soc. Jpn. 66 (1997) ) M. Mim $\mathrm{u}\mathrm{r}\mathrm{a}$ $\mathrm{m}$, H. Sakaguchi and 33) N. Kobayashi, T. Sato, $\mathrm{y}$ (2003) 970. Physica A282(2000) 283. and M. Matsushita: J. Phys. Soc. $\mathrm{j}\mathrm{p}\mathrm{n}$ 34) J. A. Shapiro: Ann. Rev. Microbiol. 52 (1998) 81. theor. $72$

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$40 $\mathrm{e}\mathrm{p}\mathrm{r}$ 45$ ro 980 1997 44-55 44 $\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{i}$ $-$ (Ko Ma $\iota_{\mathrm{s}\mathrm{u}\mathrm{n}}0$ ) $-$. $-$ $-$ $-$ $-$ $-$ $-$ 40 $\mathrm{e}\mathrm{p}\mathrm{r}$ 45 46 $-$. $\backslash