## Introduction: Fractal Antennae

Fractals are more than just intricate shapes and appealing pictures. They encompass our lives, appearing in places as tiny as blood vessels and as widespread as the patterns of tree branches. Yet, what is a fractal? Mathematically, a fractal is described as a curve or geometric figure, each part of which has the same statistical character as the whole.

As far as telecommunications, fractal-shaped antennas have greatly reduced the size and the weight of the antennas for a given frequency of use. Practical shrinkage of 2-4 times is realizable for acceptable performance, and has eliminated the need for the bulky antennas of the past.

However, fractal antennas plugged into HDTV televisions, or even other types with the aid of a converter box, can receive several local channels, free of charge and completely legal.Throughout our project, we will show you how to build your very own fractal antennas from three different materials.

## Step 1: Gathering Materials

**Description of Total List of Materials Used**

**Small Roll of Lead-Free Solder** (Most Effective)- (Quantity: 1)

**Small Sheet of Plexiglas**- 1/4" thickness (Quantity: 2)

**Roll of Aluminum Wrap**- (Quantity: 2)

**Soldering Iron and Station**- An individual Soldering Pen costs approximately half of the price of a Soldering Iron replete with a station. However, we used a soldering iron with the temperature station.

** Wood** (Squares)- Dependent on quality, but can be obtained for 38 cents per square foot. (Quantity 1)

**Roll of Insulated Copper/Silver Wire**- The cost is dependent on brand and quality. Non-insulated wire would be an option as well if it were thick enough. (Quantity: 1)

**Small bag of Screws**- (Quantity: 1)

**Manila Folder**- (Quantity: 2)

**Graphing Paper**- (Quantity: 2-4)

**Stapler** (Quantity: 1)

**Pencil**- (Quantity: 1)

**Scissors**- (Quantity: 1)

## Step 2: Calculating Costs

Because we will be exploring multiple ways of making fractals, it is not necessary to have all of the materials for each individual fractal project. For example, for a fun way to make the **aluminum foil fractals** at home, all you would need is a roll of aluminum foil, manila folders, and a stapler. If you're making the **solder fractals, **you require only the **soldering iron**, the** roll of solder**, and the **sheets of Plexiglas**. Or if you choose to make the **television wire fractals, **you would require the** screws**, **wood**, and **insulated wire.**

**The quantity, and price of all the materials is listed in the graph.**

**TOTAL ESTIMATE COST FOR ALL MATERIALS**

When averaging the costs of the items, the total amount is **110 dollars and 10 cents.**

Because we were able to attain the Plexiglas, wood, insulated wire, manila folder, and the aluminum foil, donated, and the solder iron, pencils, graphing paper, and pencils were already in our possession, our total amount spent was approximately **24 dollars. **This was the amount paid for the screws and the solder.

## Step 3: Prep: Solder Fractal Antenna

In order to build this fractal antenna, you will require the **soldering iron, solder, Plexiglas, graph paper**, and a **pencil.**

## Step 4: Choosing a Fractal Design

As Amelia and I worked throughout this project, we invested research into different types of fractals to see what would work best.Our search narrowed down to the **Koch Snowflake **and the **Sierpinski Triangle**. Either design works for all of these antennas.

When building the **Solder fractal antenna**, it is reasonable to go up to four iterations in both the **Koch Snowflake **and the **Sierpinski Triangle.**

When constructing the Al**uminum Foil fractal antenna**, it is reasonable to go up to 3 iterations in both fractal designs.

When building the **Insulated Wire fractal antenna**, it is reasonable to go up to four iterations in both fractal designs.

However, first let's go more in depth about each of these fractal types and the significance of iterations.

## Step 5: The Koch Curve and Snowflake

In order to create the **Koch Snowflake**, **Niels Fabian Helge von Koch** began with the **Koch Curve** he had already developed. The **Koch Curve** starts with a straight line that is divided into three equal parts. The middle segment is used as a base, and an equilateral triangle is formed. Then, the base of the triangle is removed, showing the first iteration of the Koch Curve.

**The Koch Snowflake** is a derivative of the **Koch Curve**. The Snowflake begins with an equilateral triangle. The steps in creating the Koch Curve are then repeatedly applied to each side of the equilateral triangle, creating a "snowflake" shape to form.

Like several other fractals, the **Koch Snowflake** is **self-similar**, projecting the same image on any scale.

The **number of iterations** is the amount of steps from the original shape of origin of the fractal. However, the original shape is generally counted as the first iteration. Holistically, we found that while a **higher number of iterations** induces **better channel reception** in both the **Solder Fractal **and the **Aluminum Foil fractal**, **a simple 2-iteration design **for the** Insulated Wire Fractal **produced the **same number of channels** as both of the **Solder Fractal Antennae.**

## Step 6: Solder Fractal Antenna: Prep Work

Before you begin, lay out the materials that were listed as necessary for this fractal antenna.

In addition, you will need to place the fractal design of your choosing under the Plexiglas to use as a guide while soldering. To get this design you can either** A: draw it by hand **or **B: print it out** from a reliable math website.

Use some sort of straight edge such as the Plexiglas if you are going to draw the designs.

## Step 7: How to Sketch the Koch Snowflake (3 Iterations)

We completed the first iteration by sketching an equilateral triangle with side lengths of six inches onto graph paper. Then we completed the next two iterations by dividing the line segment into three segments of equal length.

Next, we drew an equilateral triangle that has the middle segment from step 1 as its base and points outward.

To continue, we removed the middle line segments of sides of the resulting equilateral triangles to create more equilateral triangles.

In every iteration, the length of a side is 1/3 the length of a side from the preceding stage. As the original triangle was six in. by six in. by six in., its iterated triangles were two in. by two in. by two in. and so on.

## Step 8: How to Sketch the Sierpinski Triangle

First, draw an equilateral triangle. The sides of the triangle should each have a number of triangles that is a multiple of four. For example, you can start with a large triangle that has 16 triangles per side.

Then, divide the triangle into four smaller triangles, leaving the middle one blank.

Finally, divide all the colored triangles into four smaller triangles in the same fashion as the first one.

Leave the middle triangle of this set blank.

## Step 9: Preheat

Preheat your Soldering iron to about 750 degrees.

## Step 10: Start Soldering Your Design

Place the fractal design you chose under the Plexiglas, and place the solder metal close to the iron but not touching it directly. Follow the design with the solder and soldering iron in hand.

Note: Amelia and I attempted to solder on the paper, resulting in the burnt appearance. Before settling on Plexiglas, we attempted to solder on wood, duck tape, and manila folder. The solder was not able to stick to these surfaces.

https://www.youtube.com/watch?v=_2gCvb5XvTE

The video above shows Amelia soldering an antenna.

## Step 11: Solder Fractal and Iron Cooldown

Allow the solder fractal antenna to cool for at least 30 minutes without coming into contact with any other objects. This is to preserve the shape and self similarity of the fractal.

Next, allow the solder iron to cool for an hour before putting it away. This is for safety reasons concerning the high temperatures involved.

## Step 12: Prep Work: Aluminum Foil Antenna

In order to build this fractal, you will need **aluminum foil, ****manila folder, graph paper, a pencil, and the stapler. **

## Step 13: Constructing Foil Strips

Construct aluminum foil strips by ripping sections of foil that are about 6 inches wide.

Then, fold each strip in half, and continue doing so until each strip is about a half inch wide.

## Step 14: Constructing the Aluminum Foil Antenna

Next, fold the strips of wire along the fractal design of your choice on paper. If you chose to sketch it on graph paper as we did, you would construct along a piece of graph paper placed on top of manila folder.

In order to connect the individual strips of foil, staple at their junctions. This will not interfere with reception as the staples act as a conductor.

Now your fractal antenna is complete as it does not need to cool down.

## Step 15: Prep Work: Insulated Wire Antenna

To build this antenna you will need the **roll of insulated wire, nails, wood, and a pair of scissors.**

## Step 16: Constructing the Insulated Wire Antenna

Measure the amount of wire you need by folding it along the fractal design you choose.

Then, cut the wire, making sure live wire is exposed out of the insulation.

Screw the nails into the wood, and situate your fractal around them in a fashion where the shape of the fractal is present.

## Step 17: Plugging in Your Fractal Antenna

In order to connect your fractal antenna to a TV, you need to have wire that is exposed at the end running from the antenna jack to your fractal antenna.

In older televisions such as the one we used, a converter box is also required.

As far as attaching the wires to the aluminum foil fractal we simply maneuvered the wires underneath the foil so they were between the foil and the paper.

As far as the Solder Fractal, we used scotch tape to hold the wires in place, and we held the wires against the fractal with our hands, allowing us to experiment with the angle positioning of the fractal. We did the same thing for the Insulated Wire Fractal.

As part of our testing, we positioned the wires at different points on the fractals (Solder and Aluminum Fractal), and were met with largely the same results. In regards to even the amount of wires used, at times the reception was better when only one wire was placed on the fractal at one time instead of two. We believe this may have been the result of self interference on the part of the wires and the fractals.

Make sure that the exposed end of wire is securely attached to your antenna (tape will work), and turn on your television!

## Step 18: Amount of Time Taken

It took approximately 6 hours to test the solder and the antenna for the solder fractal, 3 hours to test the Aluminum fractal, and 1 and a half hours to test the wire fractal.

It took 1 hour to construct the solder fractal, a half hour to construct the aluminum fractal, and 45 minutes to construct the wire fractal.

It took 3 hours to brainstorm on the solder fractal, 1 and a half on the aluminum fractal, and 45 minutes on the wire fractal.

## Step 19: Possible Improvements

If we were to do this project again, we would make thealuminum wire strips thicker because it allows for better reception. To do this, we would rip off 12 inch pieces at a time and then fold them. This would be minimally difficult. We would also go to a place outside of school to further test coverage. Being inside the school allows for a degree of interference by walls and buildings. We could test this by mounting the fractal antenna on the window of a house for instance.

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## 33 Comments

Very nice work ladies! I love it when someone your age does something like this.

You might try attaching the wire to the antenna at different locations and not always the same distance away from each other or an equal distance along each path. You might also include drawings as to where you attached the wires, either I missed them or they weren't included. The old bow tie UHF antenna is a very basic fractal in some ways I guess. A full-wave-loop antenna is very similar in look to your snowflake fractal. The way it is normally attached to the radio or TV is by breaking the loop at some point and attaching both wires from the radio or TV to those two end points, one end point and one wire. I have never seen the feed line (the wire going from the radio/TV to the antenna) attached at opposite ends of an antenna as you seem to have done with your snowflake fractal antenna. In this case you may have an antenna array and not a simple loop antenna. Also, with your feed line attached to opposite ends of the snowflake you have inadvertently used part of your feed line as part of the antenna, which changes things considerably. A feed line separated and stretched out is a form of dipole antenna. The most basic of all antennas is the half wave dipole, meaning that the length of the dipole antenna is one half the wavelength of the radio frequency you want to receive or transmit. Thus, the full-wave-loop is an antenna whose length is equal to one wavelength of the frequency of interest. With TV frequencies one can never design a single element antenna capable of receiving all the wanted frequencies equally. Your fractal antenna might be able to better manage this wide frequency range requirement.

As for the triangle antenna I'd like to know how you attached the wires to it. I may have to keep this around and try some tests on it as well.

If one were to take a full wave loop already attached to the feed line and un-loop it, it could be made to look like half of your snowflake fractal antenna so, I guess in a sense, you have two stretched out and somewhat bowed "loop" antennas attached to the feed line, that's a form of antenna array, two or more antennas attached in some way. Usually multiple antennas are attached together with a phasing harness. This harness is made of feed line of a very specific length and is called phasing the antennas because the length of the wire between the two or more antennas is cut so that the signals from all antennas come together with the same phase of the sine wave signal so that they add together, thus giving the receiver a stronger signal. There are ways to phase multiple antennas so that they add signals from specific directions and decrease signals from other directions as well.

You can see some of my work on TV antennas and tests I've done on my web site and on my forum.solidsignal.com blog. The antenna I've been studying is the ubiquitous bow tie with different element lengths, separation angles and even in the quad element arrangement. The "ultimate" design is for 360 degree reception of horizontal waves that my wife named the porcupine antenna. I called it the "quad element turnstile bow tie" antenna, her name is much better :)

A full wave loop antenna has a 300 ohm impedance and a dipole antenna has a 75 ohm impedance. Most TV antennas are designed for one or the other and then changed for the TV to use if needed. That is a complete story in and of itself with no easy answer either. Older TVs had 300 ohm inputs (usually using twin-lead wire) the new TVs have 75 ohm inputs and use 75 ohm coax cable.

Porcupine antenna photos: http://cs.yrex.com/ke3fl/Articles/Antennas/BuildingThePorcupine.htm

Links to my articles on SolidSignal.com at Karras' Corner: http://cs.yrex.com/ke3fl/KarrasCorner.htm

The specific articles of the bow tie (not the turnstile version) tests are called:

Bow Tie Element Length Evaluation

Transformer Tests

Bow Tie Antenna Angle Tests

and you might also look at the "The Standard Bow Tie Antenna" article.

Keep up the good work! It looks like the two of you had great fun doing all that.

Cool project.

But, as ive found out with electrically small antennas,

Their coupling to the ether is compromised.

As such, their Q is increased, while their band width is reduced.

This is fine if youre not looking for a wide band antenna.

Not so good for UHF TV.

Then, there is the issue of matching.

Loops are higher Z and dipoles are lower Z than you realize.

When in doubt NEC it out!

I am not a engineer of any sort but AI have found the same thing that the aluminium antennas do not get all the stations. We have two different kinds of antennas and get quite a few more stations using both.

https://www.instructables.com/id/Antennas-TV-Wifi-and-etc/

PS, the only true wide band fractal antenna is the log periodic dipole array.

I've tested fractals in an anechoic chamber with a network analyzer, and they are wideband, but they can be kind of ratty, with lots of small phase and amplitude perturbations because of the fine grained elements. For small bandwidth signals you can't beat their size, and they match over a wide band. For TV, well, I have a commercial LPDA on my house. You need a nice smooth response over that 6 MHz channel to decode the signal. A bowtie is easy to make though. I've built bowties down to 3 MHz.

This is neat! So I've voted, and will go all over, because a Link to it is on this Blog of mine:

http://faz-voce-mesmo.blogspot.pt/2014/05/littlebits-farta-e-casas-de-brincar-em.html

The SOURCE sez...

Nice work!

The first fractal antenna was aluminum foil ;-)

Would there be any issue with making the insulated wire fractal and wire leading to the TV with a single long wire?

There are 2 ways you could substantially improve this project.

First, learn how antennas work. This would help you refine both your design and your testing. You can do a theoretical design based on how much signal is transmitted to your location (e.g., www.tvfool.com), and calculate how much gain you can achieve using antenna books (ARRL handbook is the cheapest) or software. You need to learn about things like matching, directivity, and polarization.

Second, learn how to test them and get useful results. With a converter box, you can read out a relative power measurement on each channel. You can compare this with a standard gain dipole that you build, and get an absolute gain measurement with decent enough accuracy. And you will learn to test in free space, not in an inside room with the antenna against your body.

I'm right there with you on this one. Antennas are much more than they appear to be.

Very cool! I made the bowtie, which works well but takes up a lot of space. https://www.instructables.com/id/Powerful-Modern-Ho... Your project would fit my available space much better. Well done!

Very interesting! I used to spend a lot of time designing and building ham radio antennas but I never tried fractal shapes. With the Sierpinsky triangle shape, I would have thought that you would have made two Sierpinsky triangles, with the triangles pointing at each other, but not quite touching. Then the antenna wires would be soldered to the two points that are near each other. It would look like a fractal bow tie. I would guess that such an antenna would behave like a bowtie antenna but would work over a larger bandwidth, especially higher frequencies.

If ham radio were not a dying hobby I would suggest you get your radio licenses and build antennas for long distance (DX) communication - it is great fun to come up with a design that really works well - suddenly you are talking to the other side of the world! Of course today, you can just open a chat box to your friend in China :-)

Have fun, and I hope you young ladies go into science or engineering - we need more female brains in those areas.

I love seeing more Koch snowflakes in the wild. Awesome!

That is very cool I'll try it one day when I've got some free time thanks

Thank you! Hope you have as much fun as we did! :)

Ok thanks I'll possibly have ago over the weekend and I'll let you know how I got on thanks again

I've put off the task for a while nice - I'll give a try

I've been trying to come up with a good antenna for a bluetooth project I've been messing with, I might try to scale some of your project down and see if I have any success. Unless, of course, you had some plans to to experiment with tiny fractal bluetooth antennae...in which case, you could do the work and I could reap the benefits. Anyway, great instructable. Triangles are my favorite shape!

I've made fractal antennae and I can say that they work best if you connect your wires between a point on the fractal that you cut. This is why you sometimes achieved better reception with only one antenna wire attached. Try the Koch antenna for example...choose a point on the antenna and cut it then connect one wire to each end. You may have to cut out a very small segment to keep the ends from shorting together, but your reception should be much better! Try it... I'd like to hear how it worked for you. PhilKe2FL also mentions this point.

well done and well written, I MUST give this a try!