# Mathematical Webcams

mercredi 1er juillet 2020
par

For all of these activities, you have to authorise the use of your webcam and stand in front of it, alone on an even background.

Dance like a function ! http://bit.ly/FunctionHero move your arms to stick to the graph of the function, as fast and accurately as possible.

#### Rules

On the 1st line, there is a list of expressions such as
sin(x),cos(x),(1/2)*x^2,(-1/2)*x^2,exp(x),(1/6)*x^3,abs(x)
You can edit this list. We call it a choreography because you are going to dance on it ! Its items are going to loop one after the other. The selected one appears as
f(x)=...
You launch a cycle of 3 loops pressing the space bar.

Standing in front of the webcam, try to position your arms so that it fits the graph of the function as quickly and as accurately as possible. You gain points for the value at the six points and the value of the derivative at the middles of the five segments. When you see the graph (in green), it’s already to late to score, be faster next time !

You score appears at the end of your cycle with a little time gap for the next user to come into play. But you can restart pressing the space bar.

There is a Reload button that allows you to generate a URL with the given choreography. This way you can challenge another group in a dance battle by simply sending a link, and bookkeeping these URLs.

This work is the main activity stemming from the PhD thesis of Pedro Lealdino Filho.

Tame Julia’s dragon with bare hands http://bit.ly/JuliaWebcam

#### Rules

Move your hands slowly. They control two points, ±√c (their mid-point is translated to the origin). The Julia set of $f_c : z\mapsto z^2+c$ is then drawn. It is the set of points whose images stay bounded under $f_c$.

Be a tree ! http://bit.ly/HommeArbre An Iterated Functions System

#### Rules

The computer computes two transformations, sending your trunk to your left respectively right arms. These are similarity transformations, corresponding to multiplying by a point of the plane, also known as a complex number. Its iterates are drawn, leading to a right and a left spiral. When you mix this system of two transformations, you get this vegetal form, looking like a fern, a bush or a stable oak tree. Explore the parameters ! Be a tree !

Similarity Master an elephant trunk with Karate.

#### Rules

The computer computes the transformation, sending your left arm to your right arm. This is a similarity transformation, corresponding to multiplying by a point of the plane, also known as a complex number. Its iterates are drawn, leading to an exploding or converging spiral. Explore the parameters ! Master the elephant trunk with Karate ! You will get a simple rotational tiling with your hands above your head for example.

Fractalise yourself ! with the conformal webcam http://bit.ly/webcamconf.

#### Rules

Choose a function in the list or write your own. You can generate a URL containing your function. Use the color points A, B, C, D and the time.