Paper Fractal Tree With Glowing Tips

Hello everybody,

This is a sculpture of a fractal tree in which I used a repeating module that scales down in size as it goes from trunk to tip. I built it by hand. You can get computer programs to generate a fractal tree but no computer is going to make it for you, as I did, out of paper. Yes, it is made from paper, cardstock to be precise.

And yes, of course, you could 3D print it but that's not me and besides, paper is more noble than plastic, don't you think? I just drew it as I wanted it then built it. It's been a lot of fun at times and at other times it's been challenging. I was very happy with how it was looking in the early stages but when I realized I had a lot of cutting and folding ahead of me I knew I was in for the long haul. Building the fractal tree was the biggest part of this project but I also sent light up through the tree that comes out the tips in a beautiful golden glow. So I needed a base to house the electrics and fold the tree firmly in place

So yeah, you might like to give it a go or you could make a smaller version with less pieces (see last two photos above). Or if you are REALLY crazy you could make an even larger version. And go on, why not, you could also make a 3D printer version :))

Supplies

Materials:

Shiny gold cardstock.

I bought these multi colored packs of shiny cardstock in a dollar store that we get here in Europe called Tedi. It's possible this amazon product is the same stuff but I'd hate to lead anyone astray. Personally, I would prefer to touch and see the paper before purchasing.

Also: glue stick, 5mm plywood, six counter sunk M4 x 15mm screws, GX53 LED lightbulb, lightbulb holder, electric cable, switch, plug etc.

Tools I used:

Craft knife, steel ruler, embossing tool, cutting mat and a computer, printer and printer paper. Jig saw, drill, contact glue, spray paint. If you have a cutting machine you could be so much faster.

Step 1: The Design

I've tried to better explain the notion that the branches are all the exact same piece in different sizes by up loading these gifs. I'm not a mathematician but I was inspired by the Pythagoras Tree fractal design where each square grows out two more squares that are set at right angles to one another. So at each junction there is a right angled triangle. Here I have made a 3D version of that idea with a right angled three sided pyramid aka: Tetrahedron at each junction, sending branches out in 3 directions. The scaled down branches follow the proportions of the golden section which kinda ties in with the use of gold paper. Also, lighting it up from the inside suggests the magic of mathematics!!!

In my design, as the branches go from one junction to the next I thought I would twist the triangular base slightly and so as a result the growth of the tree is sort of spiraling as you can see in the first photo when you isolate just one branch (in pink) of each iteration

Note: I altered the shape of the trunk in the end to accommodate the light fitting. So it's not the same as all the other branches but don't tell anyone.

Step 2: Practice Run

I started by making a small practice tree from white paper to see that everything was working well and that I got the hang of cutting, folding, and gluing everything. I made this with three different sections: the trunk, three branches , and nine smaller branches. The final composition uses a total of 141 branches of different sizes, 81 of these are just the smallest branches! So you see, there is a lot to cut fold and glue XD

By making this small practice tree I could see what technique worked best for me before starting on the real one. For example: I found it best to apply the glue inside the larger trunk before closing it, then putting the three smaller branches on top and reaching in from below to firmly press the tabs in place. See Photo no. 6 here

Step 3: Print Out the Pieces

I tried to find the best setting on my printer for the cardstock I was using. I didn't know if this was going to work I had never printed on such thick cardstock before but it printed, no problem. I needed 14 sheets for this project. I used gold for all the small sections, so the tips would shine golden. And I used silver and gold for all the other pieces only because that's what I had. If I had enough gold cardstock for the lot then that's what I would have used. Isn't it cool how in the photo here the different sizes are all proportional to on another.

The largest branch of them all (the trunk) will fit on an A4 sheet.

2 of the second largest pieces will fit on an A4 sheet.

4 of the middle sized branch will fit on an A4 sheet.

8 of the next to smallest branches will fit on an A4 sheet.

And 16 of the smallest branches will fit on an A4 sheet.

I must add, I didn't print everything out all at once. I first printed one sheet of the smallest branches and another sheet of the next size up and started to work from there. When I needed more pieces I went back and printed again.

Step 4: Cutting, Scoring and Folding

What would we do without printers! But mind you if I had a plotter I could probably run through the cutting, scoring and folding in no time flat! and not even need to print out the lines. But I don't, so I had to make do with the print outs and settled in to doing it all by hand. It was a lot of work.

First photo here shows all the pieces cut and folded, ready to make up what will be one third of the tree and another third of the tree is seen here already mounted. I did a lot of the cutting by hand, that is, without the ruler. Photo no. 2 is showing how I only cut the edges you see here in RED with a ruler. The reason being is that all other cut edges get folded inside as tabs so as long as they are more or less what I needed they need not be perfect. But the scoring was a different story.

All the folded edges got scored. This way the folds are very accurate. I timed myself to see how long it took to score all the lines in a batch of small pieces and figured each piece took me two minutes. So that's at least 282 minutes! 4 and a half hours! Just for scoring! And then there's coffee breaks, toilet breaks, go to work breaks, it seemed never ending It was the longest and most tedious part of the process. Lining up the ruler takes patients and time and I did three or four passes with the embossing tool to make the scored line deep enough. But every scored line was one less. I inched my way forward, score line after score line....

...well that's not exactly true. I kept on taking breaks from the printing, cutting and scoring to move ahead with gluing some of the pieces. Basically because I didn't know if it was going to work or not and I'm also easily distracted :))

Once the lines were scored folding them was very fast and simple.

Step 5: Glue the Smallest Branches

So, here we go. The process was the same as I went gluing all the pieces. I made sure to give the glued pieces time to set before continuing with them. But just by doing a number of pieces all in succession I was able to continue to the next steps with the gluing of the first pieces dry.

I started at the smallest branches. Glued the tabs which close the piece into a "tube" leaving one opening on the top and one opening on the bottom.

Then I joined three of them together in a triangular formation using the smaller of the two remaining tabs to glue to each other. Then I had three tabs left unglued in an equilateral triangle. Altogether there are 27 "tri-stars" like this.

Step 6: Prepare the Next Size Up

In order to glue the tabs from the triangle of tabs previously mentioned, I applied the glue to the inside of the next section as you can see here in the first photo. Then applied the glue to the tab to make the "tube" like I did before in step 5. And when I had that glued, I quickly added the trio of smaller branches and reached in from the bottom and firmly pressed the tabs. Again, letting the glue set before continuing further with these pieces.

Photo no. 3 here shows various stages of the process albeit the piece in the center is actually the paper model. From right to left, you can see how the smaller pieces join to the medium pieces and the medium to the large as the tree slowly gets bigger. I don't have a photograph like this one that includes the full tree because all the pieces go into making it up.

Last photo here is me using the rounded end of a pen to press the tabs from the inside on the last branches because they were too long for my fingers to reach the far end and too narrow to fit my whole hand inside. So I just went bit by bit from the smallest pieces to the biggest until it was all assembled.

Step 7: Finishing the Tree

This was the fantastic moment! The tree was looking amazing. However some light escapes at the corners I decided it wasn't too much of a disturbance when these gaps were small so I just left them but I did have a few larger gaps that just looked bad so I went back in there and added more glue and pressed them closed one by one.

In hindsight, if I could have found a thinner cardstock with the shinny gold finish I would have used it instead but I just went with this stuff. The shinny surface is good but the actual card was a fairly poor quality :/ leaving me concerned throughout the whole project that I would have to give up and just throw it on the fire. Not until I glued the trunk to the largest branches was I satisfied it was good enough to hold everything in place.

Step 8: Up Lighting the Inside

I needed to make a base to fit the led lamp to and also attach the tree. I made a disc from 5 mm plywood about 12 inches in diameter. I made a hexagonal hole cut out of the center to correspond with the hexagonal base in the tree. And I cut out another layer to bolt underneath the disc with countersunk screws and so the tree can be detached if necessary. I stuck the light bulb holder in place on a bottom layer and contact glued a hexagonal wall only 15 mm (5/8") in place. Then wired the cable, put in a cable trap on the exit hole and a switch and plug to finish it off. I glued some spacers under the top layer of the base that reached the bottom layer and counter sunk the screws in place. So I can open it all to be able to change the bulb if necessary. All in all, the base stayed nice and low to the floor so you hardly perceive added depth for the whole electrical installation.

And that's it I hope you enjoyed following this instructable. If anyone has any questions or comments don't hesitate to put em below I'd love to here from you. Until next time, keep on tinkering!