Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to explore number patterns in sequences and geometric properties of fractals.
Audiences:
Grades 3-5, Grades 6-8, Grades 9-12
Primary Subjects:
Discrete, Fractions, Geometry, Number and Operations
Related Topics:
decimals, fractals, fractions, geometric sequences, geometry, iteration, length, pattern, self-similarity, sequences, surface area, symmetry
Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and explore number patterns in sequences and geometric properties of fractals.
Audiences:
Grades 3-5, Grades 6-8, Grades 9-12
Primary Subjects:
Discrete, Fractions, Geometry, Number and Operations
Related Topics:
chaos, fractals, geometric sequences, geometry, iteration, length, lines, pattern, recursion, self-similarity, sequences
Step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, and explore number patterns in sequences and geometric properties of fractals.
Audiences:
Grades 3-5, Grades 6-8, Grades 9-12, Undergraduate
Primary Subjects:
Discrete, Fractions, Geometry, Number and Operations
Related Topics:
decimals, fractals, geometric sequences, infinity, iteration, lines, pre-calculus, recursion, self-similarity, sequences
Step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
Audiences:
Grades 3-5, Grades 6-8, Grades 9-12
Primary Subjects:
Discrete, Fractions, Geometry, Number and Operations
Related Topics:
algebra, area, fractals, fractions, geometric sequences, iteration, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences
Step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out. Explore number patterns in sequences and geometric properties of fractals.
Audiences:
Grades 3-5, Grades 6-8, Grades 9-12
Primary Subjects:
Discrete, Fractions, Geometry, Number and Operations
Related Topics:
dimension, fractals, fractions, geometric sequences, geometry, iteration, length, pattern, pre-calculus, recursion, recursive functions, self-similarity, sequences, symmetry, triangle
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
