Geometrics

Geometrics app for Android creates geometric patterns using polar graphing, with the help of simple controls.

Contents:

  1. Description
  2. Geometrics for Android

Description

Developer: Kyle Fischer

Category: Entertainment

Platform: Android

Submitted: 16 Oct 2014

Updated: 16 Oct 2014

Geometrics is an Android app that creates so-called Maurer rose geometric patterns using polar graphing. The geometric patterns are controlled by 3 parameters:

  • Swiping left and right
  • Swiping up and down
  • Pressing and holding

Mathematical Overview:

A "Polar Graph" is a way of representing mathematical equations. The radius of the circle is represented with the character "r", the angle that has been traversed around the circle is represented with the character "θ" (Theta). So a circle with a radius of 1 has the equation:

r(θ) = 1

A "Polar Rose" curve is a polar graph with the equation:

r(θ) = sin(kθ)

As you increase the k, each increment adds to the number of "petals" that the rose has. In this application, swiping to the right will increase the number of petals by increasing k by 1 for each swipe. (The petals actually increase by 2 on even increments and decrease by 1 on odd increments) Swiping back to the left will decrease the number of petals until you get to 1, which is the starting point circle. If you keep swiping to the left, the 2 becomes 1/2, then 1/3, then 1/4 and so on. The roses created with these fractional values are just as beautiful, have the same petal increase feature, but are not always symmetrical.

Maurer roses were introduced by Peter M. Maurer in his article titled "A Rose is a Rose" (http://en.wikipedia.org/wiki/Maurer_rose).

A "Maurer Rose" is a polar rose where we skip around the figure instead of drawing it sequentially. Instead of the angle being (0,1,2,3,4,5...), we use (0,45,90,135,180,...). Swiping up increases the number of degrees we skip by 1, and swiping down decreases the skip by 1. The app's developer has the skip number set to start at an interesting place. Somewhere around 75. Once you reach 360 degrees, you essentially start over (361 degrees = 1 degree). Certain degree skips may produce "uninteresting" patterns. 45, 90, 180 are some that may produce just a solitary line.

The app's developer also added a feature to this application where the size of the rose gets ever slightly smaller for every line drawn. This produces some of the most amazing visual effects. The app does not prevent the radius from getting below 0, it lets the radius become a negative value. You'll notice that asymmetrical patterns flip when they become negative. The radius is kept from expanding forever based on the larger of the width and height of your screen.

Pressing and holding will cycle between three modes:

  • A changeable Maurer rose that connects points to the previous point in the series
  • A changeable Maurer rose that draws lines connecting to an unchanging Maurer rose
  • A changeable Maurer rose that draws lines connecting to the same changeable Maurer rose but out of phase by a set number of degrees

Another feature added was a color fading algorithm that attempts to reach every possible color and fade between them seamlessly.

Geometrics for Android

Geometrics app for Android creates geometric patterns using polar graphing, with the help of simple controls.

Geometrics 4 seem to be the latest available version for the Android platform. Below you can find file(s) assigned to this version:

There are totally 1 version(s) of Geometrics for Android on this site. More details and all its versions are available on the Geometrics for Android portal.

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