## 3 Results
### Formation of Multicolored Patterns at Constant Voltage in the RDR Setup
The Cu\({}^{2+}\) gel: [Cu\({}^{2+}\)] = 0.200 M and 1.0 mass% agarose. The [Fe(CN)\({}_{6}\)]\({}^{3-}\) gel: [[Fe(CN)\({}_{6}\)]\({}^{3-}\)] = 0.040 M and 1.5 mass% agarose. When seen from above, the blue Cu\({}^{2+}\) gel appears green. 135 h). Interestingly, the characteristic yellow color of [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions still remained near the cathode after 90 h, suggesting that (1) the applied constant voltage of 2 V only moved [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions slowly, and hence (2) diffusion contributed significantly to ion transport, nucleation, and crystallization in the sample tube. The last image in Figure 4 was obtained after removing the unreacted ions. The yellow color disappeared, but the reddish-brown band persisted. Interestingly, the characteristic blue color of aqueous Cu\({}^{2+}\) ions also remained over a wide area at the anode side (right side), suggesting that the Cu\({}^{2+}\) ions formed sparingly soluble Cu(OH)\({}_{2}\) precipitates. The formation of Cu(OH)\({}_{2}\) precipitates in the sample tube is possible because OH\({}^{-}\) ions could be generated by a side reaction at the cathode (\(2\mathrm{H}_{2}\mathrm{O}+2\mathrm{e}^{-}\rightarrow\mathrm{H}_{2}+2\mathrm{OH} ^{-}\)) and then migrate to the anode side under the influence of the static electric field to react with Cu\({}^{2+}\) ions. Note also that the ocher color characteristic of Cu-Fe\({}^{\mathrm{III}}\) PBA was not observed, suggesting that [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions are less reactive with aqueous Cu\({}^{2+}\) ions than [Fe(CN)\({}_{6}\)]\({}^{4-}\) and OH\({}^{-}\) ions in the proposed RDR setup. It should be noted that Cu-Fe PBA can also be formed on the Cu electrodes. Figure 6a shows significant amounts of deposits at the cathode and anode after 100 h at 2 V. These deposits were firmly bonded to the electrodes, and hence the electrodes required polishing with sandpaper of different grades (#120, #240, and #400) after the experiments. Moreover, Figure 6b shows that the boundary between the [Fe(CN)\({}_{6}\)]\({}^{3-}\) gel and Cu rod is sufficiently reactive to form a small amount of reddish-brown compounds (probably Cu-Fe\({}^{\mathrm{II}}\) PBA) without voltage application. This reactivity can be explained as follows. At the boundary without an applied voltage, reactant ions of Cu-Fe\({}^{\mathrm{II}}\) PBA (Cu\({}^{2+}\) and [Fe(CN)\({}_{6}\)]\({}^{4-}\)) can be generated through the following reactions: Cu \(\rightarrow\) Cu\({}^{2+}+2\mathrm{e}^{-}\) (at the Cu metal surface) and 2[Fe(CN)\({}_{6}\)]\({}^{3-}+2\mathrm{e}^{-}\rightarrow\)2[Fe(CN)\({}_{6}\)]\({}^{4-}\) (at the gel surface in contact with Cu). At the Cu cathode/anode, the Cu\({}^{2+}\)/[Fe(CN)\({}_{6}\)]\({}^{4-}\) ions can react with electrochemically generated [Fe(CN)\({}_{6}\)]\({}^{4-}\)/Cu\({}^{2+}\) ions to produce Cu-Fe\({}^{\mathrm{II}}\) PBA precipitates. At the anode, direct electrochemical production of Fe-Cu\({}^{\mathrm{II}}\) PBA is also possible through the following reaction (for simplicity, the Fe(CN)\({}_{6}\) vacancies and the additional H\({}_{2}\)O are ignored): Cu + 2K\({}^{+}+\) [Fe\({}^{\mathrm{II}}\)(CN)\({}_{6}\)]\({}^{3-}\rightarrow\) K\({}_{2}\)Cu [Fe\({}^{\mathrm{II}}\)(CN)\({}_{6}\)] (Cu-Fe\({}^{\mathrm{II}}\) PBA) + e\({}^{-}\). Additional discussion concerning the formation of Cu-Fe PBA precipitates near/on the electrodes will be provided later. Figure 7 shows the results obtained when changing the applied voltage from 2 to 4 V. The observations are similar to those obtained at 2 V in the following aspects. (1) A single (i.e., non-periodic) reddish-brown band was formed on the cathode side. (2) A wide region on the anode side turned green. (3) The generated pattern showed almost no change after 90 h, and the gel near the cathode remained yellow.