Some informations about Some informations about snowflakessnowflakes

A snowflake is just a bunch of A snowflake is just a bunch of snow crystals stuck together, but snow crystals stuck together, but it's amazing how beautiful it it's amazing how beautiful it looks. Every snowflake is looks. Every snowflake is hexagonal and each is virtually hexagonal and each is virtually unique (although theoretically, it unique (although theoretically, it seems possible to create seems possible to create identical ones), because snow identical ones), because snow crystal bonding is affected by crystal bonding is affected by differences in dozens of differences in dozens of atmospheric conditions (i.e. atmospheric conditions (i.e. humidity, temperature, and air humidity, temperature, and air pressure, to name just a few). pressure, to name just a few). This application is a simulation This application is a simulation of the creation of snowflakes. of the creation of snowflakes. The differences in atmospheric The differences in atmospheric conditions are represented by conditions are represented by the assortment of different rules the assortment of different rules that can be used to bond the that can be used to bond the next set of crystals. next set of crystals.

HistoryWilson A. Bentley Wilson A. Bentley – „The snowflake Man”– „The snowflake Man”

From the earliest memories of our childhood, many of us can rememberhearing the phrase "no two snowflakes are alike". This discovery was made inthe small rural town of Jericho, Vermont by Wilson A. Bentley (1865-1931). A self educated farmer, Bentley attracted world attention with his pioneeringwork in the area of photomicrography, most notably his extensive work withsnow crystals (commonly known as snowflakes). By adapting a microscope toa bellows camera, and years of trial and error, he became the first person tophotograph a single snow crystal in 1885. He would go on to capture more than 5000 snowflakes during his lifetime, notfinding any two alike. His snow crystal photomicrographs were acquired bycolleges and universities throughout the world and he published many articles formagazines and journals including, Scientific American and National Geographic. In 1931 his book "Snow Crystals", containing more than 2400 snow crystal images,was published by McGraw-Hill but has long been out of print. A soft cover copy,identical in all respects, can be obtained today from Dover Publications, Inc.. OnDecember 23, 1931, Bentley died at the family farmhouse in Jericho. Because of hiswonderful work with snow crystals, he became affectionately known as "Snowflake„Bentley.

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Snowflake in MathematicSnowflake in Mathematic The snowflake curve is connected in the sense The snowflake curve is connected in the sense

that it does not have any breaks or gaps in it. that it does not have any breaks or gaps in it. But it's not smooth (jagged, even), because it But it's not smooth (jagged, even), because it has an infinite number of sharp corners in it has an infinite number of sharp corners in it that are packed together more closely than that are packed together more closely than pebbles on a beach. pebbles on a beach.

The snowflake never escapes the dashed square The snowflake never escapes the dashed square you see in figures 1-4, so it encloses a finite you see in figures 1-4, so it encloses a finite amount of area no larger than a credit card. On amount of area no larger than a credit card. On the other hand, at each step building the new the other hand, at each step building the new little triangles adds more than one unit of little triangles adds more than one unit of length to the curve. To be precise, [4 ÷ 3]n - 1 length to the curve. To be precise, [4 ÷ 3]n - 1 units are added at the nth step, so the length of units are added at the nth step, so the length of the snowflake is larger than the snowflake is larger than

3 + 1 + 1 + 1 + 1 + 1 + ... = infinity. The 3 + 1 + 1 + 1 + 1 + 1 + ... = infinity. The snowflake curve is infinitely long, yet it would snowflake curve is infinitely long, yet it would fit in your wallet! fit in your wallet!

Under a magnifying glass, a little piece of the Under a magnifying glass, a little piece of the snowflake looks identical to a larger, snowflake looks identical to a larger, unmagnified chunk. Objects that exhibit this unmagnified chunk. Objects that exhibit this kind of self-similarity are called FRACTALS and kind of self-similarity are called FRACTALS and are of great research and applied interest in are of great research and applied interest in modern science and mathematics. modern science and mathematics.

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Pivot of symmetryPivot of symmetry

It is another characteristic of It is another characteristic of the snowflake that makes it the snowflake that makes it so unique and beautiful. Take so unique and beautiful. Take a moment to look at example a moment to look at example of snowflake. Can you cut it in of snowflake. Can you cut it in half and are both sides the half and are both sides the same?same? Yes! When you observe Yes! When you observe snowflakes you notice that snowflakes you notice that they are symmetrical. All they are symmetrical. All snowflakes have 6 lines of snowflakes have 6 lines of symmetry. symmetry.

Types of SnowflakesTypes of SnowflakesNo Two Snowflakes Look The Same.There are a few reasons that no two snowflakes look the same.There are a few reasons that no two snowflakes look the same.One thing that influences the size and shape of a snowflake areOne thing that influences the size and shape of a snowflake are temperature changes: temperature changes: 30 degrees Fahrenheit (-1 degrees Celsius) - Snowflakes usually30 degrees Fahrenheit (-1 degrees Celsius) - Snowflakes usuallylook like columns. look like columns. 3 to 10 degrees Fahrenheit (-16 to -12 degrees Celsius) - 3 to 10 degrees Fahrenheit (-16 to -12 degrees Celsius) - Snowflakes are usually shaped like a star. Snowflakes are usually shaped like a star. 10 to 18 degrees Fahrenheit (-12 to -7 degrees Celsius) -10 to 18 degrees Fahrenheit (-12 to -7 degrees Celsius) -Snowflakes are usually shaped like a plate. Snowflakes are usually shaped like a plate. 18 to 23 degrees Fahrenheit (-7 to -5 degrees Celsius) – Snowflakes 18 to 23 degrees Fahrenheit (-7 to -5 degrees Celsius) – Snowflakes

areareusually look like columns appear again. usually look like columns appear again. 23 to 27 degrees Fahrenheit (-5 to -2 degrees Celsius) – Snowflakes 23 to 27 degrees Fahrenheit (-5 to -2 degrees Celsius) – Snowflakes

areareusually form a needle shape. usually form a needle shape.

What Else Affects a Snowflakes Shape?Dirt also changes the appearance of a snowflake. If a snow crystal Dirt also changes the appearance of a snowflake. If a snow crystal

spinsspinslike a top as it falls, it will usually be symmetrical when it hits the like a top as it falls, it will usually be symmetrical when it hits the

ground.ground.If a snow crystal falls sideways, then it will end up lopsided. If a snow crystal falls sideways, then it will end up lopsided.

Examples. . .Examples. . .

Some interesting details Some interesting details about Snowflakes about Snowflakes

Links:Links: http://snowflakes.lookandfel.com/ http://snowflakes.lookandfel.com/ You can use this program for make your own snowflakeYou can use this program for make your own snowflake

by internet.by internet.

http://highhopes.com/snowflahttp://highhopes.com/snowflakes.html kes.html

In that program you can learn how make paperIn that program you can learn how make paper

snowflake by yourself. You must remember thatsnowflake by yourself. You must remember that

paper snowflakes could be beautyful decoration inpaper snowflakes could be beautyful decoration in

Christmas on your Christmas tree!!!Christmas on your Christmas tree!!!

Made by Rafał Kotuła & Klaudia Damek from high school R. Schuman. POLAND