Pascals Triangle, the Sierpenski Triangle, and the Mandelbrot Set

Relation between Pascals triangle and the Sierpenski triangle

Both Pascals and Sierpenski are triangles. The Sierpenski triangle is obtained from Pascals triangle by marking or coloring the odd numbers and leaving the even numbers without color.

Properties of the Sierpenski triangle and the Mandelbrot set

Both the Sierpenski triangle and Mandelbrot set a deal with non-integer dimensions (fractal dimensions) and can be described in an algorithm. They are self-similar and are recursive.

Comparison of Pascals triangle, Sierpenski triangle, and Mandelbrot set

	Pascals triangle	Sierpenski	Mandelbrot set
Beauty	Triangular in shape.	Triangular in shape. Its ever-repeating pattern of triangles makes it beautiful	It is kidney-shaped and bordered by cardioids. When colored, the pattern is beautiful.
Complexity	It is simple to generate since the numbers of the coefficients of the previous row are added to obtain the current row coefficients.	Simple to generate since the triangles are obtained by shrinking the initial triangle over and over. 3D construction is possible.	Its generation is slightly complex since points on the complex plane have to be tested in the equation z=z²+c.
Mathematics	Binomial expansion is used to obtain its coefficients and it is used for calculating combinations or discrete values of data.	Total area of triangle tends to as triangle sizes decrease. Is used for determining logarithms, symmetry, transformations and geometric construction.	Deals with complex numbers. Plotted on the complex plane by iterating z=z²+c. Points tested must converge i.e. be <2 for them to be within the set.

Need help with assignments?

Our qualified writers can create original, plagiarism-free papers in any format you choose (APA, MLA, Harvard, Chicago, etc.)

Order from us for quality, customized work in due time of your choice.

Click Here To Order Now

Pascals Triangle, the Sierpenski Triangle, and the Mandelbrot Set

Relation between Pascals triangle and the Sierpenski triangle

Properties of the Sierpenski triangle and the Mandelbrot set

Comparison of Pascals triangle, Sierpenski triangle, and Mandelbrot set

Pascals Triangle, the Sierpenski Triangle, and the Mandelbrot Set

Relation between Pascals triangle and the Sierpenski triangle

Comparison of Pascals triangle, Sierpenski triangle, and Mandelbrot set