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# DAY 4 - APPROACHING FRACTALS WITH KIDS

In mathematics, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension. In other words, a fractal is a never-ending pattern that repeats itself at different scales (more understandable right?). This property is called “Self-Similarity.” Fractals are extremely complex, sometimes infinitely complex - meaning you can zoom in and find the same shapes forever.

Amazingly, fractals are extremely simple to make.

## Basics on Fractals

Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set. Because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self-similarity, also known as expanding symmetry or unfolding symmetry.

Fractals are found all over nature, spanning a huge range of scales. We find the same patterns again and again, from the tiny branching of our blood vessels and neurons to the branching of trees, lightning bolts, and river networks. Regardless of scale, these patterns are all formed by repeating a simple branching process. A fractal is a picture that tells the story of the process that created it.

To go into fractal details with kids, here is a very nice layman resource you can use.

## Fractals at home with kids

As we really wanted to discuss fractals with our community today, we have searched for easy activities to be made at home with kids and here are some resources you might want to take a look at, cross-cutting mathematics (obvious), art and environment observation:

Build a fractals nature suncatcher: Organise a fractal scavenger hunt (offline if possible, online you can find very inspiring pictures) to make a pretty suncatcher with one of the patterns you will find during your chase! Find the full activity here.

Infinity Mirror Level 1 - The Infinite Cat: The Infinite Cat Project is about one cat watching another cat. A long line of 1854 cats, so far. Take your camera and join the band!

We tried with our cat, and here is the result!

Discover the other cats here.

## Next level - DIY Infinity Mirror

An infinity mirror is a pair of parallel mirrors which create a series of smaller and smaller reflections that appear to recede into an infinite distance. We can make one using a strand of LEDs, a power source, a cardboard tube, and two small round mirrors, one out of acrylic and one out of “one way mirror” film used on car windows.

Here is a resource among plenty to discover this activity without programming.

### Programming and Infinity Mirror

As usual, we want to share with the community additional activities based on programming and IoT boards. Discover several resources hereunder:

1. Build an infinity mirror ring using micro:bit here

2. Build an infinity Mirror with Controllable LEDs with Arduino

3. Draw the Mandelbrot fractal using CircuitPython here.

4. And Create Art with Code - "Art is everywhere and it’s beautiful. Unleash the creative artist inside you with the beauty of Generative Art. Learn how algorithms are used to create these aesthetic art forms, how motion and structures emit sounds and what toolkits are required to do so. The talk will take the audience to a small history of Generative Art and how autonomously these art forms are created using algorithms with various examples using Processing, PyCario and more."

## Scientist of the day

Obviously, let's discover today the work of Benoit Mandelbrot, a Polish-born French and American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

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