About Geom-e-Twee

Changing between Two and Three Branches

To change the number of branches, tap 2 or 3 fingers anywhere on the display at the same time. A two-finger tap should switch to a binary Twee. A three-finger tap should switch to a ternaryTwee.

Varying the Angle by Panning and Tapping

To open or close the branches, slowly move one finger up or down on the display. This is called panning.

All angles in the Twee will change as you pan.

• Start anywhere — Pan up or down, and the angles will respond.
• Pan repeatedly (by lifting your finger) to change the angles a lot.

To make the branches open or close in steps, tap once in the upper or lower half of the display. You can tap as many times as you want, but don't tap too quickly or you'll be double-tapping! (See Gold-e-Locks Mode below.)

Varying the Common Ratio by Pinching and Spreading

To change the way the tree grows, put your thumb and finger anywhere on the display and bring them together (pinch) or move them apart (spread).

• Pinching makes interesting patterns of overlapping branches.
• Spreading makes the branches grow less, so they won't overlap.
• For more control, start with your fingers way apart.

Red prohibition signs on the display indicate that you can't pinch the common ratio any further.

To make the branches grow just right, double tap anywhere on the display. (A Double Tap is a one finger tap tap on the display.) This lets Twee's branches grow as long as they can with out touching each other. Not too long, not to short — just right. You can vary the angle while in this mode and see Twee vary the Common Ratio automatically to keep the branches reaching out just right.

You'll see a green border around the display when Geom-e-Twee is in this mode. Another double tap will turn this mode off. A pinch or spread gesture will also end Gold-e-Locks Mode.

Gesture Carefully

What to do:

• When changing the number of branches, make sure your two or three fingers tap the display at the same time. For Three - you can use two fingers from one hand and one from your other hand if that is easier.
• When pinching or spreading, put both fingers down at the same time, so that it is clear you are beginning to use two fingers to pinch or spread!
• For finer control over pinching and spreading, start with your fingers farther apart. You can move one finger or both in order to gesture. You can also use one finger from each hand for maximum spread.
• Geom-e-Twee doesn't respond well to wild gestures. Relax. You will have more fun if you let the Twee respond to your gestures — it needs more time to respond when its branches are hyper extended or it's casting long shadows.
• If you get lost, just double tap with one finger and the Twee will probably pop back to a simpler, less overlapping pattern. The angle will stay the same. If the Twee doesn't change, then it's probably already in the Gold-e-Locks Mode. (Check for a green border around the display.) You may just have to unwind the Twee angle by panning up a lot. Don't give up — geom-e-trees can be tricky! Consider checking the FAQ for help.

What not to do:

• A side-to-side gesture doesn't mean anything. The Twee may kinda look like it's doing something, but only the up-down component of a panning gesture is used.
• You may think that touching the Twee itself in some way does something. Nope. Only gestures on the display as described are meaningful.
• When single-tapping through a number of degrees, don't tap too quickly or you'll be double-tapping. See Setting and Unsetting Gold-e-Locks Mode.

Different Themes show Different Things

Color can be used for more than just making pretty patterns.

• The Rainbow themes make it easy to see what level branches are on, no matter what pose a Twee is in.
• The Zebra theme shows even-odd levels.
• The Branch Order theme shows left vs right branches in binary trees, left-middle-right branches in ternary trees.
• Allometric themes give geom-e-trees the added dimension of branch width.
• The Juggler theme shows nodes as balls. Balls on the same level are the same color.
• Twiggy and Junior Graph Theory likewise show things you don't see in any other theme.
• Other themes are just for fun.

Each theme tells us something a little different about geom-e-tree geometry.

Branch Order Theme

The first new kind of theme shows the branching order of the Twee. A binary tree's left branches are white and its right branches are black. A ternary tree has all middle branches colored dark red. The colors let you see how a Twee can curl around and fold up.

Allometric Themes

Allometric themes change the thickness of the branches as well as the branch length when the common ratio is changed. All branches on the same level have the same width. Allo-met-Twic has squared off branches, while Tweely has rounded ones. The two themes have slightly different parameters (range of values) that make them work.

The Juggler

For something completely different, we have a theme that features the nodes of the Twee rather than its branches. The underlying geometry is the same as a tree with branches, but The Juggler shows a ball at each node instead of showing the branches. Balls on the same level are the same color.

This theme is fun. We call it The Juggler because at times it looks like a clown is throwing colored balls up over his head. You may see the balls merge into just a few piles, or arrange themselves in groups. When you move away from those coincidences, the groupings explode and the balls move on their way to some other such arrangement / grouping.

Some juggling act!

More Help & Fun

On the internet...

• Visit our website! GEOM-E-TWEE.COM
• Visit Geom-e-Twee's general Help & Feedback page.
• See some wild Twees and fun puzzles on our Puzzles page (~2MB).
• Our demo Geom-e-Tree in Action is on YouTube. See Videos.
• The original Geom-e-Tree (1980) animation is on YouTube. See Videos.
• Write to help@geom-e-twee.com.

Other Time Haven Media Apps

Geom-e-Tree (website) is our all-ages app — it's even more immersive and challenging, with more branches, more lines, and more themes. Geom-e-Tree is awesome because:

• It has over 40 wild themes, including ones with pulsating colors.
• It draws trees with up to nine (9!) branches. (Twee draws two or three.)
• Tree's fine lines can create incredibly subtle patterns.
• It draws more lines for every tree.
• It has an Arboretum where you can collect geom-e-trees you've discovered.

If you've loved Geom-e-Twee and are ready to move up, download Geom-e-Tree on the App Store!

PolygonTrix (website) is a Math Art Game based on Polygonal Billiards. It's a digital arcade of angles and energy that lets you see math unfold inside polygons. PolygonTrix isn't a shooting game — it's an amusing geometric puzzler with a particle physics twist.

You can always see our current apps and other news on our mothership site: Time Haven Media Company.

Geometry may be a Universal Language...

...but please forgive our lack of Internationalization. We appreciate the friends we have in France, Germany, Spain, Italy, Japan, and other countries. Someday we hope to be able to afford professional translation of this Help and the FAQ into five or more languages and have those appear directly in Geom-e-Twee. Until then, we have provided links on our support page for Google translations.

See translations for French, German, Spanish, Italian, Japanese, etc.

Our Commitment

We'd like every child to have access to the educational and entertainment value of Geom-e-Twee. As explained above, our full-featured Tree further explores the principles you find in Twee, and demand for Tree drives our development. You can help support our work by adding Geom-e-Tree to your App collection. So, if you'd like to see Tree and Twee updates in the future, please pick up Geom-e-Tree, PolygonFlux, or PolygonTrix. Thanks for all your support!

A Challenge for other Developers

The Geom-e-Tree™ and Geom-e-Twee™ apps themselves are ©2013, by John Miller, Portland, Oregon, USA, and their app names are trademarked. These apps will have features added in later versions. We really don't want to see copycat variants of our basic design. We ask other developers to respect our right to improve Geom-e-Twee and Geom-e-Tree, and challenge them to come up with their own creative ideas to enrich the electronic playground and classroom. Thanks!