How to make a Sierpinski Christmas Tree

This Christmas tree (which is yet to be completed) is inspired by the Sierpinski triangle fractal. The image below shows the progression of the fractal at different levels of complexity.

 

The number of black triangles in each diagram forms the geometrical progression 1, 3, 9, 27, … . It is an example of a fractal, which means that it has a self-similar structure and you can see the same pattern repeated over and over again.

My challenge with Year 10 this year was to take this design into three dimensions and create a fractal Christmas tree. We started with regular tetrahedrons constructed with a pair of compasses and a straight edge. In just an hour the girls managed to create one and a half level 4 fractals each containing 4³ = 64 tetrahedrons. They worked really hard and I promised them that somehow I’d get up to the next level of fractal, which has a total of 256 tetrahedrons in it. My Year 12s and 13s helped but I was only just over half way through at the end of the day and I’m still working on it now!

This is the first one that they created:

So, this is how to do it…

1. Create the nets of four tetrahedrons and sellotape or glue them together to make a larger tetrahedron. Do this by taping three tetrahedron together on the base and adding a fourth one above.

    

2. Remember that fractals require a self-similar structure so you now need to make four of these structures and tape together to make the next stage in the fractal.

    

3. Repeat this process as many times as you like. Create four of the current structures and tape them together in exactly the same way.

I’ll post the finished tree sometime in the middle of next week, then I just have to find an appropriate place to keep it safe. It’s going to be beautiful!

[Here's a link to the finished tree - it's huge!]

Knitted Baubles

These beautiful baubles were created by Lib as part of our Christmas present this year. Now I’m definitely going to have to actually put our Christmas tree up next year. Homemade baubles and homebrewed beer – well done and thank you, Mr and Mrs Haigh!

    

My First Ever Curve Stitching - 1991

It would appear that I started curve stitching at the age of nine…

I really don’t remember doing it and I was very impressed that my work is obviously constructed accurately with a pair of compasses. I found this piece of work, which is dated on the back, in Nan’s collection of keepsakes. She hadn’t kept a huge amount but the bits and bobs she had kept were cherished.

Here are two cards that I had made for her at various times:

    

Ruth made the next one and also painted the beautiful Barn Owl (sorry about the flash) for us to give her one Christmas…