Theme for the Day: Fractals

Remember my earlier post on fractals?   Well, I'm truly hopeless at this point, so I need to share my obsession.

So what are fractals anyway?

Wiki says:  a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole, a property called self-similarity.

Well (for the non math people like me) that basically that means layers of repeated shapes that can be calculated by a formula.  But you don't need a formula to enjoy them.  Check these out:

• Fractals in nature and even in the garden 
• Fractal art gallery on Cool Math
• Also check out the wiki link for some lovely examples

Ready to make your own?  Try these cool (free!) online generators:

• "Snowflake" style - design your fractal with five straight lines
• Cool Math has five
• Easy Fractal Generator lets you draw a Julia or Mandelbrot set (or a custom one if you are mathematically inclined) and lets you export your finished work to a file for printing.  Nice.
• This generator is similar to the snowflake one above but lets you overlap fractals and export the finished work
• Sierpinski Triangle

Hands on and fun links for the younger kids:

• this pbskids.org    project 
• The fractal foundation project
• Sierpinski Triangle color page
• Sierpinski carpet (cubes) color page
• Sierpinski gear (circles) color page
• A youtube.com search for "fractals" will give hundreds of results
• Fractal your dinner with the unusual  Romanesco cauliflower (see the details here - scroll down)
• Fractal cookies!  (Okay - a brave parent will have to help with this)
• Fractals in clay  (again better to stick with fewer iterations- repeats- with the little ones)

For the older kids and the lesson planners:

• pbs.org has a wonderful fractal lesson from Nova episodes including:
• A generator
• An article on Benoit Mandlebrot
• A fractal lesson that includes an interactive and a   discussion of fractals 
• A working video link to an interesting story about fractal analysis of tapestries
• You might notice the link to the Nova episode Hunting the Hidden Dimensions which is no longer available on PBS.org.  It is available for free on Hulu however. 

• Hoagies has some recc'd some interesting sites also.

Downloads

• A caltech worksheet for the Sierpenski Triangle. Notice! This is a word doc that will want to immediately download.
• A PDF worksheet on fractal math from fractalmath.com, advanced HighSchool+
• A PDF worksheet from Randoff College for grades 5-8
• Open Source software to download. Note: I have not trialed, so use at your own risk.
• A trial copy of (not-free) fractal software. Note:  I have not trialed, so use at your own risk.

Treehouse Part 4

So back to the treehouse.  So we had glued in the top platform and decided it was way too far off the ground for a ladder to reach.  The length it was already caused it twist under our model child.  So we added a lower platform and fasten the bottom of the ladder to it.  Junior also decided that safety rails were a must so we added those as well.   We tied a strip of cloth beside the bottom platform as a climbing rope from the ground.

Lower platform, rope ladder and climbing rope.

Junior had discovered the sewing machine just before the treehouse project.   I showed him how to make simple, tiny pillows and he measured fabric against our treehouse doll and sewed several for the treehouse on his own.

Piles of pillows

pillows on the upper platform

We had just done a scout craft with melty beads and we still had them at the house, so Junior decided the treehouse needed a melty bead TV set.

Doll with her pillows and the "TV."

Next time:   The completed treehouse.

Treehouse Part 3

So we had our tree, next it was on to the platforms.

We constructed two of the standard "raft" sort of platforms out of craft sticks/Popsicle sticks fitting them into the spaces between our branches.  We picked up some bass wood* pieces to help brace the platforms against the branches wherever we could.

Building the Platforms

Upper Platform test fitting

Now here's where our math came in.   We used the easy 1:1 dollhouse scale (1 inch = 1 foot) for calculating our sizing and even had our scale model child.

"We wish to welcome you to Munchkin Land!"

Then we had a brilliant idea; make a tiny rope ladder.  We looked at real ladders and determined that rungs are about one foot apart. So it seemed easy enough: tape toothpicks to a ruler, knot some string onto each, a drop of glue to make everything stay put.  

Well...

Those tiny knots were awful and traumatic.  Keeping the string taut as you tied the knot was even worse. And the rungs kept ending up glued to the paper.  But, in the end, we had a ladder.

It's all fun and games until you glue yourself to a toothpick.

Ladder drying on tree and lower platform in progress

Clearly, the Lullaby League found it all very tedious.

We decided they had the right idea and went to 

do a little *ahem* research.

Next time, everything glued will be in place and the fun part; decorating!




*affiliate link

Treehouse Part 2

So the first step is making the "tree," by attaching the sticks to the stump.  The instructions show a half a stump, but Junior liked the look of the intact stump and we were all for less cutting.

So first we made sure the sticks were level enough to stand up, knowing they did not need to be perfect.  Then the DH began to drill two holes in the stump.  A paddle bit would have been easier but he made do with large boring bit.

Because of the guesswork involved with the drilling, we had some large gaps to deal with.

We decided to pour in a small amount of wood glue, fill the gaps with the readily available sawdust, then pour glue on top and press the mixture in. 

It was messy, but it worked surprisingly well.  By the time we were  finished all the drill holes were nicely concealed and we  were able to sand things fairly smooth again.  It did also serve to make sticks very securely fastened to the stump.

Next time:  the treehouse.

The Treehouse

I've been meaning to blog here about the Great Treehouse Project but somehow never managed to get the photos organized or set it all down in steps.

So anyway - the backstory:

I had long been enthralled with with this site but I hadn't quite got up the energy to start the project with my Cubscouts.  Then as we were moving out our school and into homeschool one of the moms proposed this project for the class.  I was immediately all over that and it became our first homeschool project.


It all started with

A Stump

and two sticks....

To be continued......

Home Made Knitting Needles

It's amazingly easy for your children to make their own knitting needles.


What you need:

• 2  12"US (or approx)  1/4"US/ 5MM diameter wooden dowel.  They generally come in 24"US lengths from the hobby/hardware store or you can get these* which are already cut to the 12" length you want. 
• 2 large wooden beads with a hole large enough to fit over the dowel or one chenille stem*.
• A sturdy pencil sharpener.

Steps:

1.  If using a 24" dowel measure and mark the center point.  Adults only: using a sharp utility blade score the line and carefully cut or break in half.   Sand the cut ends until smooth.
2. Lightly sand the length your two 12" dowels with medium and light grade sandpaper until they feel smooth in your hands.   You don't want it to snag the yarn.
3. Using the pencil sharpener carefully sharpen one end of the dowel.  You want a pencil-like shape but take care not to over sharpen.  You do not want a sharp point.  If you do find the point is too sharp, sand it until safely blunt.
4. Glue wooden bead to end the of each dowel.  If using chenille stem cut a small length for each dowel, enough to wind it around three or four times tucking sharp wire ends underneath.  Glue in place.

When the glue is dry, your new needles are ready to use!


According to this chart, your finished needle size will be:

Contemporary U.S. Size	Contemporary U.K./U.S. Metric Range	European Metric Range	"Old" U.S.(Taken from a Boye Needle gauge reprinted in a 1942 publication)	U.K.
8	5 mm	5 mm	8 (standard needles)	6

Well, now that you have your needles are you left wondering what to do?  In case you are new to knitting or just rusty, this site and this site  have some good videos to get you started.



*Amazon Affiliate Link

Picture Frames

Don’t spend the big bucks for ready-made photo frame craft kits.  Anything can be a frame with a little imagination.

The easiest?  Four extra-large  Popsicle/craft sticks or eight of the standard sized.    Or  four of each.

But you don’t have to stop there.  Check the bargain bins  at anywhere from craft stores,  to office supply stores to drug or grocery stores.

Consider:

• Sheets of craft foam
• Larger precut craft foam shapes
• plastic cookie cutters
• recycled tin can lids (provided you have a no-cut can opener* - best thing ever)
• new canning lids
• unwanted computer disks/cds
• cd cases
• wide bass wood stripes or precut wood shapes (thin)

I’m sure there are many other thoughts out there and there will be some more I will tackle in other posts.

* Link credits  my Amazon  Associates account, just in case  you love the idea too.  Honestly, I've had mine for years and years and my crafty self loves it for recycling cans.  And they didn't even pay me to say that.   Though if they wanted to, they can call me anytime.

Stained “Glass” Sun Catcher

Another craft involving crayons and heat.

What you will need is:

• old crayons
• waxed paper
• a clothes iron

Instructions:

1. Prep:  take crayons and make them into a fine shavings.  A crayon shaperner is the easiest way to do this.
2. I usually separate the colors into little paper cups or and old egg carton.
3. Give each child a piece of waxed paper and fold it in half so there is a crease.
4. Have child sprinkle crayon shavings on one half of the paper.  Don’t let shavings get to close the edge.  Allow a margin of around an inch.
5. When finished have an adult carefully fold the paper along the crease and place on a heat safe surface.
6. Cover the paper with a towel and iron over it on the cotton setting.
7. Remove towel.  The crayon shavings should have melted into something resembling stained glass.
8. Let paper cool before lifting it.  It could burn you or the wax can run out the edges.
9. The paper can now be trimmed out and a hanger added.
10. Hang in a window or a sunny spot.  Keep out of a very warm place so the wax won’t re-melt.

My Favorite Craft

I’m starting things off with my favorite craft ever.    This was devised by my mom and we loved it as kids.  My kids love it just as much.   It’s quick, easy and fairly mess free.  It does involve a burn risk, so caution is needed.

The main downside is that it requires some specialist equipment.   Namely, an old fashioned electric hot plate.  They just don’t make them like they used to.  My mother kindly passed down her  vintage 1970s hotplate to me.  But I found these examples on eBay.

A Salton Hot Plate

A Cornwall Hot Plate

If you can get your hands on one of these gems, then all you need is some old crayons,  aluminum foil,  and plain copy paper.

1. Cover surface of  the hot plate  with aluminum foil.
2. Plug in hot plate and let it get warm.
3. Have the child draw a design on the foil using crayons.  Keep hands away from the foil surface and the hot plate.  The crayons will melt onto the foil.
4. Once the child is finished, lay a sheet of copy paper over the drawing.  Smooth down carefully – don’t burn yourself!
5. Lift paper.  Drawing is now on the paper.
6. Put aside to dry.

Easy!  Once they have tried it, kids will ask to do this again and again.

Tips for success

• Don’t use words (unless you can write backwards!)
• Keep the drawing the same size as the paper  – some hot plates have a large surface
• Foil will need to be wiped down or changed every few drawings.  If you opt for the wipe down method, use a damp towel you don’t care about.  Remember – melted wax.
• Have fun and experiment.   More enthusiastic artists will find that crayon wax will pool and colors will ooze together in interesting ways.

Happy Crafting!