Aligned Resources

Introduces the basic ideas needed for understanding functions.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Discrete

Related Topics: addition, algebra, arithmetic, dependent, functions, independent, input, integers, linear functions, multiplication, output, pattern, subtraction, variable

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 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