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2 briefly describes the experimen- tal procedures. A full description of the experimental results follows in section 3. Conclusions and discussions of the results are presented in section 4. Preliminary results of this work have been reported in ref. [19]. 2. Experimental procedures Experiments are quite simple, as shown below. Careful attention should be paid to avoiding contamination by miscellaneous bacteria and fungi. First of all, we chose Bacillus subtilis as the sample bacterial species. The reason for the choice is as follows. Bacteria are unicellular organisms, and the species Bacillus subtilis is rod-shaped with about 0.7 ~m diameter and

2 Ixm length, and proliferates through the simplest cell division. This enables us to study most clearly the effect of environmental conditions (nutrient concen- tration, agar moisture, temperature, and so on) on the colony formation. One more advantage to use this bacterial species is that it is hydrophobic and tends

500 M. Matsushita and H. Fujikawa / Diffusion-limited bacterial colony growth to grow two-dimensionally on the surface of agar plates, which enables us to analyze colony patterns much more easily. The bacterial strain was isolated from food and identified as Bacillus subtilis. We used the same strain through- out the present experiments. A solution of

5 g of sodium chloride,

5 g of potassium phosphate dibasic and a certain amount of Bactopeptone (Difco Laboratories, Detroit, USA) as nutrient was made in

1 liter of distilled water, and adjusted at pH 7.1 by adding

6 N hydrochloric acid. The solution was then mixed with

15 g of Bactoagar (Difco). The mixture was heated at 121°C for

15 min to autoclave it and then

20 ml of it was poured into each plastic petri dish of

88 mm diameter. After being kept at room temperature overnight, the agar plates were dried at 50°C for about

40 min. The thickness of the agar plates thus prepared is about

3 mm. The bacterial strain was inoculated on the agar plate surface at the center of the dish. The plates were stored in a humidified box at 35°C. Bacterial colonies incubated and grown on agar plates for a while (typically three weeks) were photographed through transmitted light. The photos were then analyzed digitally by a personal computer through an image scanner to obtain the fractal dimension by means of the box-counting method. 3. Experimental results The colony patterns grow two-dimensionally on the agar plates, since the species used in the present experiments (Bacillus subtilis) is hydrophobic. The effect of nutrient concentration was investigated first. Fig.

1 shows colony patterns incubated three weeks after inoculation at various initial nutrient concentrations. Maximum colony size in the figure (fig. lc) is about 2.5 cm. An increase of the nutrient concentration is found to enhance the colony growth. Particularly, the growth does not take place without nutrient, as seen in fig. la. This means that the local bacterial proliferation (local growth process) at the interface of colonies is governed primarily by the presence of nutrient. It should be noted that already in fig. lc the colony pattern exhibits an outwardly open and randomly branched structure, clearly reminiscent of a two-dimensional DLA pattern. From now on we fix the initial nutrient concentration at I g/l. (Note that this concentration is much less than usual, e.g.,

15 g/l.) In fig.

2 a typical example is shown of colony patterns incubated three weeks after inoculation at this nutrient concentration. It really looks like a two-dimensional DLA pattern. In fact, its fractal dimension measured by the box-counting method is about 1.72. Averaged over