# Geometrics PRO

"Lots of relaxing fun. you can become absorbed in the endlessly changing patterns and colors and allow them to rest your mind. An aid to meditation. I highly recommend this app."

"I love the ability to create awesome art with just a few strokes of color.pretty smart idea to have. Cool!"

"If you love geometry and you love color, you will love this app! When starting the app, it begins with one of the configurations, which builds on itself and grows until you exit or, by swiping the screen in any direction, you begin a new configuration. Totally mesmerizing!"

Create stunning geometric patterns with 3 simple controls:
* Swiping left and right
* Swiping up and down
* Pressing and holding.

View samples on flickr http://www.flickr.com/photos/geometricsapp/

Mathematical Overview:
A "Polar Graph" is a way of representing mathematical equations. The radius of a circle is represented with the character “r”, the angle that has been traversed around the circle is represented with the character “θ” (Theta) where 360 degrees completes a circle. 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 Geometrics, 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 ¼ and so on(I have skipped values for k of 0 and less than 0 because a 0 k value produces a single point and the negative k values have a positive k value counterpart that produces the same picture. The roses created with fractional values are just as beautiful, have the same petal increase feature, but are not always symmetrical.
Maurer Roses:
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.
Pressing and holding will cycle between three modes:
* A Maurer rose that connects points to the previous point in the series.
* A Maurer Rose pattern defined by k and dTHETA that draws lines connecting to a different Maurer Rose equation defined by k2 and dTHETA2.
* r(θ) = tan(kθ). Which is the same as r(θ) = sin(kθ) / cos(kθ). So as cos(kθ) approaches 0, the radius approaches infinity. This produces a very interesting pattern with no maximum radius since it goes to infinity on occasion.
As we draw the patterns, we attempt to fade through each color with a unique color fading algorithm I created.
If you press the menu button, you will have the following options:
* Save the last image to the SD card.
* Set Properties Manually
- k:
- dTHETA (change in θ):
(The second k and dTHETA will automatically be reset to match the first k and dTHETA when you press and hold and cycle to the 2nd pattern type. This is because there are a very large number of "uninteresting" patterns with this pattern type and I wanted to start off with a pattern that has symmetry.)
- Image width and Height
(Be careful with this setting. Initially, I set your width and height to the smaller of your width and height in pixels. Some phones/tablets are not friendly to very large image manipulation. I have had good luck setting my image width and height to 2000 pixels, but after swiping left or right, the application does a force close because of some memory issues. I am currently working on this problem 2/25/2012)

Recent changes:
Jelly Bean devices can now save images to external storage.
\$0.99
86
4.3
User ratings
3
Installs
50+
Concerns
0
File size
810 kb
Screenshots

"Lots of relaxing fun. you can become absorbed in the endlessly changing patterns and colors and allow them to rest your mind. An aid to meditation. I highly recommend this app."

"I love the ability to create awesome art with just a few strokes of color.pretty smart idea to have. Cool!"

"If you love geometry and you love color, you will love this app! When starting the app, it begins with one of the configurations, which builds on itself and grows until you exit or, by swiping the screen in any direction, you begin a new configuration. Totally mesmerizing!"

Create stunning geometric patterns with 3 simple controls:
* Swiping left and right
* Swiping up and down
* Pressing and holding.

View samples on flickr http://www.flickr.com/photos/geometricsapp/

Mathematical Overview:
A "Polar Graph" is a way of representing mathematical equations. The radius of a circle is represented with the character “r”, the angle that has been traversed around the circle is represented with the character “θ” (Theta) where 360 degrees completes a circle. 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 Geometrics, 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 ¼ and so on(I have skipped values for k of 0 and less than 0 because a 0 k value produces a single point and the negative k values have a positive k value counterpart that produces the same picture. The roses created with fractional values are just as beautiful, have the same petal increase feature, but are not always symmetrical.
Maurer Roses:
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.
Pressing and holding will cycle between three modes:
* A Maurer rose that connects points to the previous point in the series.
* A Maurer Rose pattern defined by k and dTHETA that draws lines connecting to a different Maurer Rose equation defined by k2 and dTHETA2.
* r(θ) = tan(kθ). Which is the same as r(θ) = sin(kθ) / cos(kθ). So as cos(kθ) approaches 0, the radius approaches infinity. This produces a very interesting pattern with no maximum radius since it goes to infinity on occasion.
As we draw the patterns, we attempt to fade through each color with a unique color fading algorithm I created.
If you press the menu button, you will have the following options:
* Save the last image to the SD card.
* Set Properties Manually
- k:
- dTHETA (change in θ):
(The second k and dTHETA will automatically be reset to match the first k and dTHETA when you press and hold and cycle to the 2nd pattern type. This is because there are a very large number of "uninteresting" patterns with this pattern type and I wanted to start off with a pattern that has symmetry.)
- Image width and Height
(Be careful with this setting. Initially, I set your width and height to the smaller of your width and height in pixels. Some phones/tablets are not friendly to very large image manipulation. I have had good luck setting my image width and height to 2000 pixels, but after swiping left or right, the application does a force close because of some memory issues. I am currently working on this problem 2/25/2012)

Recent changes:
Jelly Bean devices can now save images to external storage.

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