## 3 Results
### Formation of Multicolored Patterns at Constant Voltage in the RDR Setup  
Figure 4 shows the spatiotemporal evolution of a multicolored pattern formed in the sample tube using the proposed RDR setup at an applied constant voltage of 2 V for 100 h (plus an additional monitoring period of 50 h without voltage application). The top of this figure illustrates the charges of the electrodes and the directions of reactant ion movement induced by the electric field. After 15 h of voltage application, a faint, short reddish-brown band formed at -8 mm from the cathode surface. After 40 h, the color of this band became deeper, suggesting the accumulation of Cu-Fe\({}^{\text{II}}\) PBA (see Figure 2). The boundary of the band became clear on the cathode side, and its position did not change over the observation time (100 + 50 = 150 h). After 40 h, a wide region on the anode side became green. Typically, aqueous Cu\({}^{2+}\) ions give a blue color in gel/solution, but they could appear green when mixed with [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions, which give a yellow color (Figure 5). Thus, the green color in the sample  
Figure 3: Spatiotemporal evolution of a precipitation band of Cu-Fe\({}^{\text{II}}\) PBA formed at 25 \({}^{\circ}\)C in the conventional RD setup under the following initial conditions. Outer electrolyte gel: [Cu\({}^{2+}\)] = 0.250 M and 1.0 mass% agarose. Inner electrolyte gel: [[Fe(CN)\({}_{6}\)]\({}^{4-}\)] = 0.025 M and 1.5 mass% agarose. The elapsed time after the addition of the outer electrolyte sol is indicated at the right of each image. The arrow at the bottom indicates the position of the gel boundary. Figure 2: Well-developed precipitation patterns of Cu-Fe PBA formed at 25 \({}^{\circ}\)C in the conventional RD setup (schematically shown in Figure 1a) under the following initial conditions. Outer electrolyte gel: [Cu\({}^{2+}\)] = 0.250 M and 1.0 mass% agarose. Inner electrolyte gel: (a) [[Fe(CN)\({}_{6}\)]\({}^{4-}\)] = 0.025 M and (b) [[Fe(CN)\({}_{6}\)]\({}^{3-}\)] = 0.025 M, both with 1.5 mass% agarose. The elapsed time after the addition of the outer electrolyte sol was 135 h.  
tube suggests the accumulation of aqueous Cu\({}^{2+}\) ions without generating Cu-Fe\({}^{\text{III}}\) PBA, which are typically ocher (Figure 2b). After 65 h, the reddish-brown band, which was not periodic but continuous, propagated toward the anode by \(\sim\)3.5 mm in the movement direction of the [Fe(CN)\({}_{6}\)]\({}^{4-}\) ions, and the green color at the anode side deepened. The reason why the precipitate front propagated only toward the anode side is not clear currently. However, one possible cause is that, on voltage application, [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions (as well as [Fe(CN)\({}_{6}\)]\({}^{4-}\) ions generated from the cathode) become depleted near the cathode over time as a result of their transport to the anode side, thus preventing the precipitation of Cu-Fe PBA near the cathode. Meanwhile, such depletion is less likely at the anode side. After 90 h, the pattern was well-developed and showed almost no further changes, even after stopping the voltage application at 100 h (compare the images taken at 90 and  
Figure 4: Spatiotemporal evolution of a multicolored pattern formed at 25 \({}^{\circ}\)C in the sample tube using the proposed RDR setup under an applied constant voltage of 2 V. The initial conditions are as follows: [[Fe(CN)\({}_{6}\)]\({}^{3-}\)] = 0.050 M and 2.0 mass% agarose. The elapsed time after voltage application is indicated at the right of each image. Bottom image: the pattern after removing unreacted ions. A scale bar is provided at the bottom of the image. Top: illustration of the charges of the electrodes and the movement direction of reactant ions induced by the electric field. Figure 5: Side and top views of a beaker in which an agarose gel containing Cu\({}^{2+}\) ions was placed atop an agarose gel containing [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions at 25 \({}^{\circ}\)C for 300 s. The initial conditions of these gels are as follows.