# Infinite Fractal Surrounded by Fractals

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## Introduction: Infinite Fractal Surrounded by Fractals

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Is there
anything cooler than fractals?

In this Project we decided to apply our love for fractals by combining two of them in a wall lamp. As an introduction, the ones we chose are the Mandelbrot set made with a 3D printer and the Lichtenberg fractals, fancy shapes created with electricity.

However, you may be wondering what a fractal is. The definition of fractal a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

The Mandelbrot set is generated by iteration, which means to repeat a process over and over again. In mathematics this process is most often the application of a mathematical function. For the Mandelbrot set, the functions involved are some of the simplest imaginable: they all are what is called quadratic polynomials and have the form f(x) = x2 + c,

where c is a constant number. As we go along, we will specify exactly what value c takes.

To iterate x2 + c, we begin with a seed for the iteration. This is a number which we write as x0. Applying the function x2 + c to x0 yields the new number

x1 = x02 + c. Now, we iterate using the result of the previous computation as the input for the next. That is

x2 = x12 + c x3 = x22 + c x4 = x32 + c x5 = x42 + c and so forth.

Lichtenberg figures (German Lichtenberg-Figuren), or "Lichtenberg Figures", are branching electric discharges that sometimes appear on the surface or in the interior of insulating materials. Lichtenberg figures are often associated with the progressive deterioration of high voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within insulating materials often provides engineers with valuable insights for improving the long-term reliability of high voltage equipment. Lichtenberg figures are now known to occur on or within solids, liquids, and gases during electrical breakdown.

The branching, self-similar patterns observed in Lichtenberg figures exhibit fractal properties. Lichtenberg figures often develop during the dielectric breakdown of solids, liquids, and even gases. Their appearance and growth appear to be related to a process called diffusion-limited aggregation (DLA). A useful macroscopic model that combines an electric field with DLA.

Due to this amazing physics phenomena we decided to make our Project based on fractal sets and figures with recycled materials.

By combining an infinity mirror and a Lichtenberg figure we created this project.

### Supplies:

Wooden board

Wooden box

Glass mirror

Tainted glass

Microwave transformer

Car clamps

Nails

Water and Baking soda

Glue

Glass foil

LEDs

2 Batteries

Tape

Wires

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## Step 1: Switch on the Lights

For this first step we
used the microwave transformer with the car clamps attached one to the main current supply and the other car clamp to the chasis of the microwave transformer. To make the Wood conductive we had to dilute the baking soda and the water. We conclude that the more saturated the mix is, more conductive. This may be kind of danger to the fractal because it burns too quickly and the fractal is not made properly. Once the mix was set along the Wood, we plugged in the transformer and let the fractal be made. By the way, to make a Good contact with the Wood we put a nail in the tip of the car clamp.

After the fractal is made, Wood needs to be cleaned.

To create the infinity mirror we built a box without covers. We burnt the edges in order to get the Lichtenberg figure so the box fits perfectly the plywood.

There are some things to consider when doing an infinity mirror. After creating the box we glued the glass and the mirror together. Then we attached to the structure some recycled leds from a balloon. The inside of the box had to be black so we painted it. When we got the glass tainted and everything fitted well, we just got to screw the infinity to the plywood but that's one of the last steps, since we need to finish the plywood circuit.

## Step 2: Build the Infinite

with fractals, we decided to put a Mandelbrot fractal in the middle of the mirror.

The first thing to do is to drill the holes in the plywood, so we can attach to the plywood some LEDs (we used uv LEDs). All the circuit, the batteries and the infinity mirror wiring is at the back of the plywood. Once we got the holes and attached to the plywood the LEDs, we started mixing the e-poxy with some spray Paint. We choosed fluorescent orange.

When the plywood finally dried, it was time to solder all the circuit and finish the project.

We got issues while solding the LEDs because some of the e-poxy filtered through the holes, but the LEDs still conductive. It was pretty simple to make it work as is a regular LEDs series wiring.

After this step all we got to do was mixing both of them with screws.

## Step 3: Put Everithing Together

And there it is, a cool wall lamp to guide you through the fractals and beyond maths.

By Eduardo Cachero and Nadia Brzostowicz

Participated in the
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