Ask Dr. Math

High School Archive

Browse High School Fractals

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Coastline of Britain [02/13/2002]

Is it true that the coastline of Britain is infinite?

Complex Numbers and the Mandelbrot Set [12/15/1996]

Can you tell me about the Mandelbrot set?

Fractals [11/9/1994]

We are doing a project on fractals. Is there any way that you could help us understand what they are about? We have read all types of books and don't understand what they are saying. Could you explain them in regular English for us?

Making fractals [7/8/1995]

How do you make a fractal?

Sierpinski Triangle [01/09/1997]

What is Sierpinski's triangle?

What is a Fractal? [04/01/1997]

What are fractals? Who first used the term, when, why, and give at least two specific examples.

Applications of Iteration [05/29/1997]

What are some of the applications of iteration?

Chaos Theory and Computers [2/4/1996]

I have happened upon an equation which can create a fractal that demonstrates chaos theory graphically. Since the computer cannot learn, and chaos theory is based on a lack of pattern, how is the computer able to compute this?

Definition of Fractal [01/17/2005]

What is the definition of a fractal? Would a circle be considered a fractal?

Determining Equable Shapes [06/15/1999]

Could you please list some equable shapes and show me how you determined them?

Fractal Dimension of a Coastline [01/16/1997]

How do you measure the fractal dimension of a coastline?

Fractal Dimensions [01/10/1998]

How do you calculate the fractal dimension of a fractal?

Fractal Image Compression [05/27/1997]

How do you use fractals?

Fractals, Complex Numbers, and Chaos [01/20/1997]

Do fractals have anything to do with complex numbers? Do they have something to do with chaos?

Fractals in Real Life [10/04/1999]

How are fractals used by scientists and mathemeticians in the real world today?

Generating Fractal Equations [7/1/1996]

Is there any way to generate a fractal equation from a set of numbers?

Introduction to Fractals [09/02/1998]

Can you give me some basic information on fractals? How would you create one?

Is the Coastline of Britain Infinite? [08/17/1999]

According to Mandelbrot's theory of fractals, the coastline of Britain is infinitely long. Can you explain this?

Limited Area, Unlimited Perimeter [11/27/1997]

What is the figure?

Limit of Area [03/01/1998]

Limit approached by area of a square when its sides are repeatedly divided into three congruent parts and squares are constructed outwardly on the middle parts.

Mandelbrot and Julia Sets [06/29/1998]

Can you explain how Mandelbrot and Julia sets are formed?

Mandelbrot Set [10/23/1996]

What is the Mandelbrot set?

The Math Behind Music: Pitches, Scales, Geometry [12/03/1997]

Connections between music, physics, and math.

Perimeter and Area of the Koch Snowflake [12/02/1998]

How do you prove that the Koch Snowflake has an infinite perimeter but a finite area?

Projective Geometry [01/13/1997]

When seen from a semi-bird's eye view, a fractal terrain looks like a regular trapezoid. When rotated right or left, the four corners seem to move along an ellipse. Find the equation of the ellipse whose center is also that of the trapezoid.

Sobre Fractales [11/22/1996]

Quisiera saber una manera de conseguir material en matemática sobre fractales.

Sources For Information About Fractals [2/16/1995]

Where should I look to learn about fractals?

Van Koch Snowflake Perimeter and Area [10/31/1998]

If the Van Koch's snowflake process is repeated indefinitely, find the perimeter and the area, given an initial area 'A'.

What Kind of Math are Fractals? [10/23/2004]

Can you tell me what branch of mathematics includes fractals?

Why Do Recursive Rational Functions Attract and Repel? [07/10/2008]

Given a recursive linear rational polynomial with two roots, if you recursively apply f(x) the function will converge to one of the roots. Why does the function have a preference to one of the roots? How can you determine the attractor root other than trial and error?

Z Values in the Mandelbrot Set [04/27/2006]

Could you please explain why for the Mandelbrot set the modulus for the resulting z value must remain less than 2?

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