EL001 Metallic Tree/Voronoi Diagram

This is a common method introduced in various experimental guides and books. With numerous variations available, we will present an example of a copper tree experiment using copper sulfate solution and a zinc plate.

Equipment : petri dish, filter paper
Reagents : copper(II) sulfate solution (0.5 mol/L), zinc pieces (5–10 mm square)

　Methods
　　　① Take 5 mL of copper(II) sulfate solution and transfer to a petri dish.
　　　➁ Place filter paper in a petri dish to soak the entire surface.
　　　➂ Place a piece of zinc on a piece of filter paper and observe the formation of a copper tree over time.

The growth of the metal tree can be observed with the naked eye, but using a microscope allows for a detailed examination of the fractal structure of the metal tree.

The growth rate of the metal tree varies depending on factors such as the concentration of metal ions in the solution, the type of anions, and the type of metal piece used. Select the reagents and conditions that suit the available materials and the time allotted for the experiment. Below are some examples:

0.5 mol/L copper(II) sulfate solution + zinc pieces
(from left to right: immediately after placement, 5 min, 10 min, 15 min)

0.1 mol/L copper(II) sulfate solution + zinc pieces
(from left to right: immediately after placement, 5 min, 10 min, 15 min)

0.5 mol/L copper(II) sulfate solution + aluminum pieces
(from left to right: immediately after placing, 5 min, 10 min, 15 min, and 3 days later)

0.5 mol/L copper(II) chloride solution + zinc pieces
(from left to right: immediately after placement, 5 min, 10 min, 15 min)

Metal trees created in standard experiments are typically very fragile and can collapse with even slight vibrations. However, this issue can be resolved by solidifying the metal ion solution with agar. One notable feature of this method is that the metal crystals can expand three-dimensionally.

　Equipment：Beakers (100 mL and 200 mL)
　Reagents：copper(II) chloride (0.5 mol/L aq), zinc plate, powdered agar-agar, sugar

Methods
① In a 200 mL beaker, add 1 g of powdered agar and 50 mL of copper(II) chloride aqueous solution. Heat the beaker to dissolve the powdered agar.
② Once the powdered agar is dissolved, add 75 g of sugar and heat while stirring to dissolve it completely.
③ Pour the agar solution from step ② into a 100 mL beaker and let it sit until it cools to room temperature.
④ Place a zinc plate bent into your desired shape into the beaker from step ③, then cool it in a refrigerator or in ice water.
⑤ Once the agar has solidified, leave it at room temperature for several days.

Metal trees can grow even without adding sugar, but the agar may appear cloudy, making it necessary to carefully arrange the placement of the metal pieces.

Alternatively, you can add 20 mL of glycerin instead of sugar.

A Voronoi diagram is a diagram that divides a space into regions based on the proximity of multiple points (called seeds or generators) placed within a given metric space. Each region consists of all the points closer to a particular seed than to any other (citation: Wikipedia). Voronoi diagrams are used in urban planning and can also be observed in natural patterns such as the markings on giraffes, turtles, and dragonflies.

By using agar and multiple metal pieces, it is possible to create a Voronoi diagram pattern from the spread of metal trees around each metal piece.

Equipment : petri dish (inner diameter 85 mm), plastic wrap, permanent marker, beaker, copier paper
Reagents : powdered agar, silver nitrate, copper pieces (5 mm square)

Methods
① Add 10 mL of water and 0.2 g of powdered agar to a petri dish, then heat to dissolve the agar.　　　
② Once the agar is completely dissolved, add 0.8 g of silver nitrate, stop heating, and quickly stir with a glass rod.

③ After letting it sit for a while and allowing the agar to solidify, place a copper piece on an appropriate spot on the agar.

④ Cover the petri dish with plastic wrap and mark the same position as the metal piece with an oil-based pen.
⑤ Place a sheet of copy paper over the plastic wrap and transfer the marks from the wrap onto the paper using a pencil or ballpoint pen.　　　
⑥ Using the points on the paper as a reference, create a Voronoi diagram.

⑦ Observe the silver tree once it has sufficiently grown (the photo shows the state after 3 days, but it will grow sufficiently after just 1 day).

⑧ Place the paper from step ⑥ under the Petri dish, and compare the boundaries of the Voronoi diagram you created with the boundaries of the silver tree.

As you can see in the image, the grown metal trees do not touch each other. It’s quite mysterious.