A Smoking Red Squirrel

One of the red squirrels moved into the garage for the winter. Amelia didn't like that. It was in the ceiling of one of the rooms in the house and in the attic. A squirrel has moved in every winter and I didn't know what the problem was (oh, Amy told me what the problem was). The dogs go nuts in the garage trying to track the squirrel, and the last insult was when it stole and chewed a pack of cigarettes. I became worried about squirrels smoking in the house, so I agreed that Amy could try to trap it in my havahart trap. Twice, the squirrel retrieved the peanut butter bread and closed the trap but never was itself trapped. The third time was the charm. Today, my little squirrel was safe inside the trap.

Here is the little rascal patrolling her snow tunnels in the back (taken through window). I'm taking bets on how long it will take her to move back into the house.

Blog update: my blog is not loading at all today. I have had only 10 visitors instead of the normal 100-200. I apologize for this but I don't know why it is happening. And as you know, Google Blogger has no way to directly e-mail for help. You have to jump through hoops to find out anything and I don't do that. If this situation doesn't improve, I'll be moving the blog.

Technorati Tags: red squirrel, Tamiasciurus hudsonicus, havahart trap 

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Wordless Wednesday: Ducks

Mallards for sure. Mergansers also? I don't know.

Taken at the outlet of Crystal Lake, Barton, Vermont.
More photos of the lake and Hardscrabble Mountain from today.

The outlet goes to Crystal Lake Falls in Barton Village.

Above and below, an old ice house.
There should not be open water in mid-January.

When clicked, these photos will open, full size, in a new window.

Please click on the photos to see them full size in a new window.

Visit more participants by clickingWordless Wednesday
Thank you for visiting.

Technorati Tags: Wordless Wednesday, mallard ducks, Crystal Lake, Barton, Vermont
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Unplugged Project: Mancala, Continued

It was Ski Day at school but many students didn't go. I had three different sets of students painting my Mancala egg cartons today. It will take a few days for them to dry because they are saturated in paint.
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Cats Tuesday: Winter Cats (and Dogs)

Buddy wakes up for about an hour or so a day to play with his scrunchy ball.

Scout does not like to sleep with any cat.

Charlie sleeps more than Buddy does.

Sophie (dog) and Mouse (cat) are still in love.

By the way, Sophie caught and killed a mouse on her daily walk in the woods today. The mouse died quickly and humanely, unlike when a cat catches a mouse.

Thank you for visiting.
To visit other participants, visit Gattina or click Cats on Tuesday
Happy COT!

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Digital Photography Assignment 1.2: Scenics: Missisquoi River

I was excited when I took these photos. I thought they would be beautiful. Yet I never, ever, noticed that I was in shadow. None of these are any good. But I'm not going to have the time to return to the site and retake this set. I will submit them in the assignment. It'll be a good example of what to look out for. Why didn't I notice this?

All photos will open in a new window, full-sized, when clicked.

Technorati Tags: Missisquoi River, Troy, Vermont
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Photo of the Week: St. Louis Daily Photo Blog: Art Walks On Eight Legs

St. Louis Daily Photo Blog: Art Walks On Eight Legs

For that digital photography class that I am auditing, I have to look at photos and discuss one: why I like it, inspiration, etc. This is one that I will be using. The only problem? Nobody I know has a color printer and if they did, would the color be reproduced accurately? Anyhow, I'm going to use it. There are many points in it for me to discuss: the lighting, the people in the foreground, the sculpture, St. Paul's Cathedral, how the sculpture pops out. How I want to learn Photoshop and take better photos.

Go take a look.

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Today's Bird Photos: Chickadees

Technorati Tags: black-capped chickadee, Parus atricapillus,
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Unplugged Project: Mancala

Update here.

Cut egg cartons apart to make your own Mancala game. Paint them or cover with pretty papers and you have a custom made and worthwhile game that two people can play. I am making mine for my classroom. I have cut apart the egg cartons and will have students at school paint them with paints that the art teacher feels would work best. The only other thing I need for the games are 24 little stones for each game. I may use beans or poker chips that I have at school because stones are rather difficult to find under a few feet of snow.

I piled them up in front of Possum's little countertop bed and she isn't sure if she likes this. (I had to use this opportunity to post a couple of the few good photos I get of this girl.)

What is Mancala? It is an ancient game from Africa that is mathematically significant for your children to learn. I am not even going to bother any of us with the mathematics but if you like, you can have your children talk about strategies the will increase their chances of winning. It is a rather complex game to learn, but once you learn you become addicted. I used to know how to play years ago but I had to learn all over again in order to write this post. You cannot overemphasize the importance of game playing for mathematics learning and for family relationships.

If you click the Mancala Snails image above, you will be taken to an online, free version of Mancala. It is the easiest way to learn how to play. Just choose "beginner lever" and play until you begin to develop strategies. There are many variations of the game, but stick to the basics that are in Mancala Snails. The rules used there are accurate and true to the real game. It is said that Mancala is the historical precursor to chess. I know for a fact that children love to play this game because they always ask me to get one for the classroom. Now I enjoy playing the computer at Mancala Snails when I am tired and just want to relax.

Possum is still a bit startled by the mess about her and hopes I take the cartons to school in the morning.

Thank you for stopping by.

Visit other participants of the Project at Unplug Your Kids
or clickUnplugged Project

Next week's Project: Pipecleaner (or Twist Tie? Or Wire?)

Technorati Tags: mathematics games, Mancala, Mancala Snails, Unplugged Project, sowing games, combinatorics
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Digital Photography Assignment: Scenics I: Willoughby Gap

First set of five of scenics assignment.

Lesson: delete photos by formatting your memory card. Not from the computer software. There are relics of images always left on the card unless you re-format.

Learned: I shoot crooked.

Technorati Tags: Willoughby Gap, Willoughby Lake, Westmore, Vermont
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Friday Fractal: Lesson 1: Achilles and the Tortoise

I want to understand fractals better, and in the hope that somebody else also wants to, I am going to post each lesson that I complete. I have chosen to study the Introduction to Fractals: Infinity, Self-Similarity and Recursion published by Shodor. There's no special reason why I chose this lesson. But because I did, we will reviewing Zeno's Paradox. There are several paradoxes of Zeno but basically they argue that you can't travel anywhere at all because you can divide the distance to an object in half and in half again and again and never quite reach it. That is a very quick and dirty summary of the paradoxes. To learn the details, read the Wikipedia article Zeno's Paradoxes. More on the paradox in this lesson later.

First, we need to define some words. Keep these definitions around because we will be using them for the next five lessons. If there is a link attached to a word, it will take you to a Shodor "discussion" of the topic (in a new window). Since we want to start our learning nice and easy, we are going to read these discussions thoroughly.

Vocabulary

• fractal: a term coined by Benoit Mandelbrot in 1975, referring to objects built using recursion, where some aspect of the limiting object is infinite and another is finite, and where at any iteration, some piece of the object is a scaled down version of the previous iteration
  
• generator: the bent line-segment or figure that replaces the initiator at each iteration of a fractal.
• infinity: Greater than any fixed counting number, or extending forever. No matter how large a number one thinks of, infinity is larger than it. Infinity has no limits
• initiator: a line-segment or figure that begins as the beginning geometric shape for a fractal. The initiator is then replaced by the generator for the fractal.
• iteration: repeating a set of rules or steps over and over. One step is called an iterate.
• logarithms: the exponent of the power to which a base number must be raised to equal a given number. An example: 2 is the logarithm of 100 to the base 10. One can look at this way: 10 * 10 = 100, which is the same as 10^2, and 2 is the exponent referred to above.
  
• recursion: given some starting information and a rule for how to use it to get new information, the rule is then repeated using the new information
• self-similarity: two or more objects having the same characteristics. In fractals, the shapes of lines at different iterations look like smaller versions of the earlier shapes

My Reading and Notes:

• Properties of Fractals Discussion: Mandelbrot used the word "fractal" because in Latin, fractus means broken. Mandelbrot viewed these things as being highly irregular and crinkley. Another good reason to use the word fractal is that they have fractional dimension. See, also, notes on plane figure fractals discussion below.
• Dimension and Scale Discussion: Dimension, Scale and Number of copies: Scale ^ Dimension = Number of copies.
• Exponents and Logarithms Discussion: most calculators have a button built in to calculate logs. The Koch Snowflake is not one dimensional or two dimensional but somewhere in the middle. On a calculator, E12 on the end says to move the decimal point 12 spaces right. When we use the log base e we call it the Natural Log (ln). I'll need to refer to this discussion a lot.
  
• Plane Figure Fractals Discussion: things all fractals have in common: (1) All were built by starting with an "initiator" and "iterating" using a "generator." So we used recursion.
  (2) Some aspect of the limiting object was infinite (length, perimeter, surface area) — Many of the objects got "crinklier." (3) Some aspect of the limiting object stayed finite or 0 (area, volume, etc). (4) At any iteration, a piece of the object is a scaled down, otherwise identical, copy of the previous iteration (self-similar).
• Infinity and Iteration Discussion: The sum of an infinite number of numbers can be finite. Think about the tortoise and hare race: The tortoise travels the following distances, one fraction for each time step: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + . . . but never gets to the end of the race! So the sum above never gets past 1. AND So when we ran the tortoise and hare race, each time I press the advance button in the Tortoise and the Hare I am iterating: repeating a rule over and over again. So I must find the rule (it looks like the rule is half your distance each step). AND infinite sums --> calculus --> limits. AND "repeat infinitely many times:" means let the number of iterations approach infinity.
  
• Recursion Discussion: recursion: a special kind of iteration. It's a rule for moving to the next stage. Fibonacci sequence is generally extended with a recursive rule (add the previous two numbers to get the next term).
  
• Self-Similarity Discussion: it's a property of the object, not of the steps used to build the object. Iteration and recursion frequently result in self-similar objects. Hilbert Curve is a self-similar object, but the way we construct it is an iterative process.
  
• Trees As Data Structures Discussion: outcomes, probabilities, binary trees, how to make many dimensional trees, and logarithms! Cool stuff! Keep for the future. It ties all the stuff in school together, now I know why it's all important in my classes.
  
• Wikipedia: Zeno's Paradoxes (take what you can and leave the rest)

I played with the Tortoise and Hare applet and recorded the results so that I could complete the worksheet. I immediately recognized the race as one of Zeno's paradoxes and had a lot of fun with it. Here are my results:

Neither runner gets to the finish line. The differences in speed and length run are powers of two. The rule seems to be to cut the distance in half in each time unit. My right-most column in the spreadsheet is not labeled or formatted correctly because it is for only one racer. If you drop the data down one row, the differences are identical for the hare.

I knew the graph would be a curve and would approach one. I drew fitted lines for each runner and they intersected somewhere between 11 and 12 or something (I can't see it clearly and didn't take the time to figure it out but it would be easy enough).

The graph of the speed of each runner: they approach zero. The runners' fitted lines intersect between 10 and 11.

Worksheet Questions:

Who is ahead after 5, 10 and 15 time steps? By how much? The tortoise is always ahead by 1/2 of the distance he was ahead by before.

Who is running faster? Calculate the average speed of the tortoise and the hare during each of the first four stages. Remember that the average speed can be measured as change in distance divided by change in time. What is happening to the speed of the tortoise and the speed of the hare as the race progresses? The hare is running twice as fast as the tortoise. The speed of each is cut in half at each time unit. They are going slower and slower at each time marker.

Will the tortoise or the hare ever win? No.

Conclusion: each runner cuts his speed in half at each time marker. The distance between them decreases by half of the amount from the time before. They will never reach the finish.

This concludes Lesson 1, Activity 1 of my exploration of fractals. I had a lot of fun, reviewed algorithms, and learned a nice way to teach multi-dimensional trees. One of my favorite parts of this first lesson was the mathematics of dimensions (the Koch snowflake has a dimension between one and two). The math was easy but the concept bends my brain! Cool stuff. Wish I had a Zeno Doughnut!

Friday Fractal

Technorati Tags: Zeno's Paradox, fractals, Tortoise and the Hare, logarithms, iterations, recursion, generation, self-similarity, iteration, data trees, initiator, generator
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Common Redpolls

The shrike was here at dawn. But redpolls, chickadees, bluejays and red squirrels flocked to the feeders in the morning. They have to know where it is or its schedule in order to appear like this. I haven't seen the redpolls for a month. There were four today.

These photos will open, full-sized, in a new window when clicked.

Technorati Tags: Common Redpoll, Carduelis flammea
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Snowmobiling in Westmore

I'm auditing a digital photography course and was out taking scenic photos when these snowmobilers politely crossed my path. There were many of them out around Willoughby Lake north beach. Not as good a photograph as you see done with huge cameras, but my only and my best so far.

Technorati Tags: snowmobiling, Northeast Kingdom, Westmore, Vermont
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LOL Cat Bible: Lectionary Readings for the Third Sunday After Epiphany

Third Sunday after Epiphany
Isaiah 9:1-4
Psalm 27:1, 4-9
(Ps. 27:1)
1 Corinthians 1:10-18
Matthew 4:12-23

These are the verses of today's lectionary readings that have been translated:

Psalm 27

Of David.

1 Oh, hai! CEILING CAT is my cheezburgr.
who i iz scard of?
CEILING CAT is my kitteh bed—
who i iz scard of ffs?

2 Wen skript kidehs DOS me
to nok me offline
when trols n lusers atak me w/ teh BFG,
tehy wil trip on it.

3 If a crew raid me,
I not chikn;
even if tehy stole my bike,
i stil rulz!

4 One thing I askz 4, O CEILING CAT, plz,
this is what I luk 4. Ready?:
cheezburgrz
evry dai, srsly,
yumy laik CEILING CAT's beleh fuz
cuz cheezburgrz bring me closer 2 u kthx.

5 For wehn Brian Peppers cums 4 me
CEILING CAT keepz me sayf;
he hidez me in his tabby-nacle
n putz me on top of book shelf.

6 Then i iz lookz down on nmes
above the nmes taht suround me;
at his tabby-nacle I will sacrifice a mouse w00t!;
I will sing "We Are teh Champyons" 4 CEILING CAT.

7 Hear me meow, O CEILING CAT,
DO NOT WANT u 2 pwn me. Hit me up on mesenger plz.

8 I getz feelin i sposed 2 fynd ur fuz face r sumptin,
Ur fuz face, CEILING CAT, I luks 4.

9 No hydz ur fuz face frm me plz,
no get pised of @ me plz;
cuz u hav helpd me ffs.
no putz me on ignor list,
O CEILING CAT.

10 Even if mom n dad kill filter me,
CEILING CAT wil readz al my emailz.

11 Teach me skilz, O CEILING CAT;
show me how 2 pwn
skript kidehs.

12 Do not giv tehm r00t on my servr,
cuz tehy sez tehy pwn me already ffs,
ther breath stinkz of hot pokets n diet pepsi.

13 Im shur:
I wil seez teh fuzy beleh of CEILING CAT
b4 I diez.

14 Wait for CEILING CAT;
hez comin srsly
wait for CEILING CAT kthx bai.

1 Corinthians 1:10-18

Divisions in the Ceiling Cat Clubz
10 Evribodi get along plz?
11 bcz Chloe telled on u! OMG u r fightin!
12 I iz tryin sai: one d00d sez "me follaz Paul"; differnt d00d sez "me follaz Apollos"; third sez "me follaz Cephas"; An sum othr d00d "me follaz Christ!" Srsly WTFBBQ!
13 Christ iznt in bite-size chunx! Is Paul on cross for u? NO! U wuz givn bath for Paul? NO and also OMG waterz!
14 I iz glad I not gived u bath! (xcept Crispus An Gaius)
15 so nobodi can sez anybodi gotted bath in mai namez (xcept Crispus An Gaius).
16 (OK I gived Stephanas An his families bath. N maybi some1 else, I forgets.)
17 enniwai Christ didn't sended me to giv u bath! He sended me 4 telling you good newses about Ceiling Cat! An I duz not do that wif smart human wordz! Bcz that meanz Christ's cross haz no powerz! oh noes!!!

Ceiling Cat iz Smartr than U
18 Msg 4m cross 2 teh dyin: i iz just silly. msg 4m cross 2 us who iz being savedz: i iz the powr of Ceiling Cat!

Matthew 4:12-23

Jesuz begunz 2 preech, amirite?
12 Wen Jesus founded out dat John wuz in prison he made tracks fr Galile
13 An staid in Capernaum at teh c-side bt he dint tak his bukkit an spayd.
14 Cuz teh wize Esaias sed
15 “In all teh base, laik Zabulon n Nepthalim n teh c n Jordan (yeh even KT Prys) n Galilee.
16 Jesus will turn on teh liteswitch fr teh kittenz dat iz sittin in teh dark."
17 Dat iz wen Jesus strted 2 tell teh kittenz, “repent cuz teh kngdom of heaven am at hand btw.”

The callin of teh frist desipels
18 Den Jesus bumpded into 2 broz hoo wuz fisherzmen n wuz called Simon AKA Peter n Andrew AKA Lil’ Bro
19 N Jesus sed, “Comes wit me n u can b manfisherz.”
20 N cuz Jesus am teh 1337, dey wuz laik, “kthx.”
21 N den Jesus met James n John, hoo wuz chillin on a bote wit dair pops, hoo wuz Zebedee frm teh Magic Roundabout.
22 N dey also went wit Jesus.

Jesuz heels teh sIckly
23 Jesus tuk hs crew roun Galilee, teechin in teh tmples n preechin teh gospel n heelin teh sick.

moar funny pictures

HALP!
We hope to have many other Holy Kitties featured this year.
Please e-mail your photo to me at meeyauw[at]gmaildotcom
with the subject "Holy Kitties."

If you would like to help translate for the LOL Cat Bible,
please go here.

Board the Friday Ark at The Modulator (submit your post here)

Weekend Cat Blogging #138 Jan 26-27
The Tuxie Cats at Tuxedo Gang Hideout
(see the week’s host to enter your WCB
post in the comments for the weekend roundup)

Bad Kitty Cats Festival of Chaos at
Pet & The Bengal Brats at Pet’s Garden Blog
Optional Theme - Feathers Or Birds
(submit your post here)

The Carnival of the Cats #202 is going to
Bad Kitty Cats Sunday Evening
(submit your post here)

Visit the Pet Prayer & Praise Blog

Technorati Tags: LOL Cat Church, LOL Cat Bible, Lectionary Readings, Prayer & Praise Blog, Weekend Cat Blogging

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Friday Fractal: NLVM Mandelbrot and Julia Sets Applet

The National Library of Virtual Manipulatives at Utah State University has a Mandelbrot and Julia Sets applet that is your first resource for playing with fractal images. Instead of making my own fractal image this week, I have skitched some images for you to peruse and perhaps use in your classes. We have no time to do this in our regular classes but they would be a fun introduction for children in an after school program or math club.

Be sure to read the instructions and the Parents and Teachers files (I have closed the sidebars with these files on these skitches).

The first skitch above shows the Mandelbrot set. There is only one Mandelbrot set. You can zoom into a portion of the image by dragging your mouse over the section you are interested in. It appears in the right hand window. You can then drag in the right hand window to further zoom in and it will appear in the left. Students will observe that the entire Mandelbrot set is reproduced again and again as you zoom in further and further.

Although there is only one Mandelbrot set, there are an infinite number of Julia sets. Julia sets are fractals: there is one Julia set for every point on the Mandelbrot set. Select the Julia Sets option and you will see a Julia set in the left hand window. You can zoom in on this fractal by dragging your cusor over the image. The zoomed image will appear on the right. You can also move the cursor on the coordinate plane that appears so that you can see what happens to the set in the different areas of the plane.

Above you see a zoomed image of a Julia set.

On the last option, you can explore the relationship between the Mandelbrot set and Julia sets. You will see the Mandelbrot set on the left. Shift-click on an area in which you are interested and the Julia set for the point that you selected will appear on the right. You can zoom with your cursor on either window.

I hope that you explore and enjoy this applet. It can help you understand the images that I make and you can begin to make your own with third party software.

Friday Fractal

Technorati Tags: National Library of Virtual Manipulatives, Utah State University, fractals, Mandelbrot sets, Julia sets
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