Cynthia Lanius

Table of Contents     Introduction   Why study fractals?     What's so hot about     fractals, anyway?   Making fractals     Sierpinski Triangle          Using Java          Math questions          Sierpinski Meets Pascal     Jurassic Park Fractal          Using JAVA          It grows complex          Real first iteration          Encoding the fractal          World's Largest     Koch Snowflake          Using Java          Infinite perimeter          Finite area          Anti-Snowflake             Using Java   Fractal Properties     Self-similarity     Fractional dimension     Formation by iteration   For Teachers     Teachers' Notes     Teacher-to-Teacher   Comments     My fractals mail     Send fractals mail   Fractals on the Web     The Math Forum   Other Math Lessons     by Cynthia Lanius   Awards     This Site has received

What's so hot about fractals, anyway? They're New! Most math you study in school is old knowledge. For example, the geometry you study about circles, squares, and triangles was organized around 300 B.C. by a man named Euclid. Much of fractal geometry, however, is much newer. Research on fractals is being carried out right now by mathematicians. Have you ever thought about a career as a mathematician? You can understand them. Much research in mathematics is currently being done all over the world. Most of it is extremely complicated. Although we need to study and learn more before we can understand most modern mathematics, there's a lot about fractals that we can understand. Objects in nature often look fractal in structure. Most objects in nature aren't formed of squares or triangles, but of more complicated geometric figures. Many natural objects - ferns, coastlines, etc. - are shaped like fractals. Here you can read about fractals in nature. There are some really cool concepts connected to fractals. Imagine that the picture at the top of this page is a picture of the coastline of Africa.You measure it with mile-long rulers and get a certain measurement. What if on the next day you measure it with foot-long rulers? Which measurement would give you a larger measurement. Since the coastline is jagged, you could get into the nooks and crannies better with the foot-long ruler, so it would yield a greater measurement. Now what if you measured it with an inch-long ruler? You could really get into the teeniest and tiniest of crannies there. So the measurement would be even bigger, that is if the coastline is jagged smaller than an inch. What if it were jagged at every point on the coastline? You could measure it with shorter and shorter rulers, and the measurement would get longer and longer. You could even measure it with infinitesimally short rulers, and the coastline would be infinitely long. That's fractal. People use them to solve real-world problems. Engineers have begun designing and constructing fractals in order to solve practical engineering problems. For example take a look at Amalgamated Research Ic.'s Fractal Control of Fluid Dynamics. Internet Research Questions: You can find the answers from the sites linked above. Who organized geometry into a series of books? What are those books called? What is the name of a mathematician who does research today? Where does he/she work? What is the area of mathematics in which he/she works? Find another picture of a fractal that looks like an object in nature.

. Copyright 1996-2007 Cynthia Lanius