Aligned Resources

Introduces all of the 2 variable function and prisoner/escapee notions necessary to understand the Mandelbrot set.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: chaos, complex number, coordinate, coordinate plane, coordinate system, division, escape, exponents, fractals, functions, geometric sequences, geometry, infinity, iteration, julia set, mandelbrot set, multiplication, pattern, planes, prisoner, radius, recursion, recursive functions, self-similarity, sets, symmetry

Enter a complex value for "c" in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: complex number, coordinate plane, coordinate system, fractals, iteration, julia set, mandelbrot set, recursion, recursive functions, sets

Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.

Audiences: Grades 6-8, Grades 9-12, Undergraduate

Primary Subjects: Algebra, Geometry, Graphs, Number and Operations

Related Topics: complex number, coordinate plane, coordinate system, exponents, fractals, functions, graph, infinity, iteration, julia set, mandelbrot set, recursion, recursive functions, sets