## 2 Materials and Methods
### Preparation of Gel Samples and Optical Microscope Observation  
The sample tube filled with agarose gel containing [Fe(CN)6]3- ions was prepared as follows. K3[Fe(CN)6] powder was dissolved in deionized water at 25 \({}^{\circ}\)C to form a 0.050 M [Fe(CN)6]3- solution (30 mL). After adding 2.0 mass% agarose, the mixture was stirred vigorously at 98 \({}^{\circ}\)C for 30 s to produce a uniform [Fe(CN)6]3- agarose sol. Note that the density of the employed agarose sol was very high in order to suppress gel shrinkage when a voltage is applied. Using a Pasteur pipette, the prepared sol was transferred to plastic straws (4 mm diameter and ~50 mm long), whose bottoms had been plugged by Cu rods (HIKARI, CM395-4; 4 mm diameter and ~20 mm long), which were used as the cathodes. Because the sol was viscous and solidified quickly (within 1000 s), it did not leak from the bottoms of the straws. Plastic straws were employed as sample holders because they are simple to process and use, low-cost, highly transparent to X-rays, and allow the easy introduction of viscous samples [24]. The hot sol in the straw was allowed to cool to 25 \({}^{\circ}\)C, thus forming a solidified gel. The height of the gel column in the sample tube was ~40 mm. Another Cu rod (HIKARI, CM395-3; 3 mm diameter and ~20 mm long) was placed atop the gel as an anode. This Cu rod was narrower than that at the tube bottom. Because it did not fit tightly inside the straw, the Cu anode could maintain contact with the gel surface even when the electric field caused the gel sample to contract. The cathode and anode were connected to a programmable power supply (1696B, B&K Precision, Yorba Linda, CA, USA). During volugle application at 25 \({}^{\circ}\)C for 100 h (current < 1 mA), the precipitation patterns formed in the sample tube were monitored using a digital camera (IXY650, Canon, Japan). The formed patterns were further monitored for 50 h without voltage application, and thus the total observation time was 150 h. The voltage application period of 100 h was chosen because the precipitation patterns showed almost no further changes after ~90 h of constant voltage application. We monitored the sample tube for another 50 h, because the precipitation patterns formed under cyclic alternating voltage conditions sometimes changed noticeably after stopping the applied voltage (as will be shown later). After monitoring the formed pattern, the gel sample was pulled out of the straw and repeatedly immersed in deionized water (~200 mL) until the water no longer showed the characteristic yellow color of unreacted [Fe(CN)6]3- ions. This soaking process typically took 3 days. The gel sample was then placed in the straw one more time and plugged at both ends by styrene-resin stoppers covered with Parafilm. The repacked gel sample was examined using an optical microscope (SKM-S31C-PC, Saitoh Kougaku, Japan) and then mounted on a handmade holder (acrylic resin, 80 mm \(\times\) 30 mm \(\times\) 10 mm (\(h\times w\times d\))) for X-ray fluorescence (XRF) experiments. For comparison, the conventional RD setup (illustrated in Figure 1a) was also used to produce precipitation patterns of Cu-Fe PBA in agarose gels (1.0-2.0 mass% agarose). In this case, gel columns containing [Fe(CN)\({}_{6}\)]\({}^{3-}\) and [Fe(CN)\({}_{6}\)]\({}^{4-}\) ions were separately prepared in glass tubes (4 mm diameter and 60 mm long) in a manner similar to the above description. These gel columns were employed as the inner electrolyte gels, their height was \(\sim\)35 mm, and the concentration of [Fe(CN)\({}_{6}\)]\({}^{3-}\) or [Fe(CN)\({}_{6}\)]\({}^{4-}\) therein was 0.010-0.100 M. For the outer electrolyte gel containing Cu\({}^{2+}\) ions, CuCl\({}_{2}\cdot\)2H\({}_{2}\)O powder was dissolved in deionized water at 25 \({}^{\circ}\)C. After adding 1.0 mass% agarose, the mixture was vigorously stirred at 98 \({}^{\circ}\)C for 30 s to prepare a uniform Cu\({}^{2+}\) sol (0.100-0.500 M).