Maths & Art in Computer Science @efeme66 - Tumblr Blog

QR Fun & Arts

QR Codes

QR Code (abbreviated from Quick Response Code) is the trademark for a type of matrix barcode (or two-dimensional code) first designed for the automotive industry. More recently, the system has become popular outside the industry due to its fast readability and large storage capacity compared to standard UPC barcodes. The code consists of black modules (square dots) arranged in a square pattern on a white background. The information encoded can be made up of four standardized kinds ("modes") of data (numeric, alphanumeric, byte/binary, Kanji), or through supported extensions, virtually any kind of data.

Structure

Encoding

QR Codes and Arts

Recently, QR codes base structure, has been used to produce different visual approaches to these graphics. I found some online application where we can try some interesting effects.

Fancy QR Codes Generator

QR Arts

Iris flower data set

The first picture was created with Parallel Sets software. It is a new way of visualising data and understand it.

Last picture was created with Many Eyes and can be customised online at this URL: http://www-958.ibm.com/software/data/cognos/manyeyes/visualizations/iris-data

The Iris flower data set or Fisher's Iris data set is a multivariate data set introduced by Sir Ronald Fisher (1936) as an example of discriminant analysis. It consists in a data set to quantify the morphologic variation of Iris flowers of three related species (Iris setosa, Iris virginica and Iris versicolor). The data set consists of 50 samples from each of three species of Iris, considering four features from each sample: the length and the width of the sepals and petals, in centimetres. It is probably the most used data set for testing in many classification techniques in machine learning such as support vector machines. The use of this data set in cluster analysis however is uncommon, since the data set only contains two clusters with rather obvious separation. One of the clusters contains Iris setosa, while the other cluster contains both Iris virginica and Iris versicolor and is not separable without the species information Fisher used.

Data source:

http://archive.ics.uci.edu/ml/datasets/Iris

http://en.wikipedia.org/wiki/Iris_flower_data_set

http://www.r-statistics.com/tag/iris-data-set/

Software

http://eagereyes.org/parallel-sets

Some of my experiences with images and diverse effects, playing with characters and Hilbert curves.

#Hilbert Curves #Characters

my Hilbert experiences

Hilbert Curves German mathematician David Hilbert discovered the curve that bears his name in the early 1900's. It is an example of a "space-filling" curve: it literally covers every point in a square. Like fractals, it is generated in iterations. Hilbert with Ladders(below) is output generated from a modified Hilbert algorithm that also draws other shapes and ladders at points along the Hilbert Curve. The Hilbert space filling curve is a one dimensional curve which visits every point within a two dimensional space. It may be thought of as the limit of a sequence of curves which are traced through the space. The basic pattern is a curve which starts near the bottom left corner of a box and terminates near the bottom right corner. It has a kink in it, the kink takes it into the top left and top right of the box. Don Relyea, based on Professor Cumming of Napier University, Edinburgh, UK works and with a small amount of effort adding several of his drawing routines, was able to generate fantastic results. http://www.donrelyea.com/hilbert_algorithmic_art_gallery.htm If you like to try yourself, it is possible to it here:

http://www.donrelyea.com/space_curve_generator.htm

#Hilbert Curves

MATHS II

Nature by Numbers

The Golden Ratio and Fibonacci numbers

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure illustrates the geometric relationship.

Expressed algebraically, (a+b)/a = a/b = φ where the Greek letter φ represents the golden ratio. Its value is,

Relationship to Fibonacci sequence

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, … If we divide two consecutive numbers os this sequence, 1/1 = 1 2/1 = 2 3/2 = 1.5 5/3 = 1.6666666(7) 8/5 = 1.6 13/8 = 1.625 ... we will obtain the special number,

1.61803398874989484820458683436563811772030917980576286... = φ In Nature

We won't find Fibonacci numbers everywhere in the natural world. Many plants and animals express different number sequences. But, Fibonacci numbers appear in nature often enough to prove that they reflect some naturally occurring patterns. You can commonly spot these by studying the manner in which various plants grow. Here are a few examples:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

Seed heads, pinecones, fruits and vegetables. Look at the array of seeds in the center of a sunflower and you'll notice what looks like spiral patterns curving left and right. Amazingly, if you count these spirals, your total will be a Fibonacci number. Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pinecones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner.

http://science.howstuffworks.com/environmental/life/evolution/fibonacci-nature1.htm

Voronoi III

Voronoi II

A Voronoi diagram is a special kind of decomposition of a given space, determined by distances to a specified family of objects (subsets) in the space. These objects are usually called the sites or the generators (“seeds”) and to each such object one associates a corresponding Voronoi cell, namely the set of all points in the given space whose distance to the given object is not greater than their distance to the other objects. Voronoi diagrams can be found in a large number of fields in science and technology, even in art, and they have found numerous practical and theoretical applications. It is the technique that enables the division of such multi-dimensional spaces into subspaces.

source: Wikipedia

Examples:

http://mbostock.github.com/d3/ex/voronoi.html http://www.cs.cornell.edu/home/chew/Delaunay.html (applet)

Voronoi example programs (Voro++)