Math: Fractals

What is a fractal?

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.            (Definition taken from this site:  Fractal Foundation)

I made a fractal snowflake,

a fractal munchlach,

and a cactus.

Fractals are fun.

Math: Symmetry and Mirrors

(Photos taken and narrated by Jadon, typed by mommy)

So this is when I tried to take a picture of a circle but the flash was on.  Still looks pretty cool.  

This one I turned off the flash.  I drew a straight line and used the mirrors to make the line into a circle.

Then, I made a square.  A really small square.

This is the top view of the square.  This is made from just one small line.  The mirrors made more lines to combine into a square.

Now, I made a triangle.  I took the mirrors and made them even wider to make the triangle and did it from a side view.

I then made a line you can make into a house.

This is two lines.  I thought it would make a bigger square but it just made two lines when I made the mirrors like a book.  

Then I made angles by putting the mirrors on an angle on the line that I drew.

This is a paper that I thought it would make it look cool.  It made it look like a snowflake.

Here’s the other paper that I thought was cool.  It made it look like a donut.

I found some lined paper and made a spider web.  Happy Halloween!

Math: More Symmetry

Snowflakes are symmetrical.

If you fold a paper in half and cut the shapes, the shapes are the same on the other side.  That’s symmetry.

Or you can do lots of folds and when you open it, it shows a lot of what you cut out.

There’s also symmetry in nature.  The water reflects the trees.

Math-Symmetry

(Narrated by Jadon.  Typed by mommy.)

What is symmetry?

Jadon:  So, there’s a butterfly and symmetry is that one side of the butterfly is the exact same as the other side.  They mirror each other.

This one looks like a moth.

This one looks like a flying centipede.

This one is a butterfly.

This one looks like a rib cage.  Skeleton.

This was fun painting and folding and learning about symmetry.