Geom-e-Tree Frequently Asked Questions

Thank you for coming to the FAQ for Geom-e-Tree 1.3.
  • Just so you know - We are painfully aware that Geom-e-Tree has not been updated for some time! (painfully.) We have new themes and even a new icon, but we got side-tracked for most of 2014 - the centennial of Martin Gardner's birth. We will go back to Trees and such in 2015.
  • Be sure to also see the end of the Explore page for many good discussion and research questions.
  • If your question hasn't been asked before or answered satisfactorily, please feel free to write to TimeHavenMedia @


Q: Why/When does a red prohibition sign appear on the display?

A: Short Answer: The symbol appears when the common ratio (CR) is being restricted. (Earlier versions put a red border around the display when CR was being restricted.)

Pinching decreases the CR, while spreading increases the CR. In most themes, only pinching is constrained. The Allometric Themes also have spreading constrained.

Longer answers (more on why): In most themes, the the app lets you make the branches as short and stubby as you want, but constrains the branches to doubling in length from level to level. This doubling happens when the common ratio reaches 0.5, and then you can go no lower — at 0.3333…, branches would triple in length from level to level, 0.25 would make them quadruple. There is nothing inherently evil about branches getting geometrically longer, but we decided to limit the pinch because the Trees tend to make pinwheels with radiating arms that you already can see at 0.5. A lot of lines get drawn over other lines, and the drawing slows down. Maybe we will have an option for lifting constraints in a later version.

The Allometric themes are more explosively geometric and need more constraint because they expand in area, not just length. If unconstrained, your gestures could easily cause the drawing to cover the display with layers upon layers of black, and, as currently programmed, the app would stall if this happened. Ergo the constraints, and the red prohibition symbol.

Q: How can I print?

A: At this time, you can save a Tree to Photos, then sync your photos and print from iPhoto. You can also use Apple's printing service in iPhoto to order prints from your photo album.

You can also make an Apple greeting card from any Tree you have in iPhoto!

From Geom-e-Tree, you can to Email a Tree to yourself, save it out of Email and print however you print images from Windows, Mac OS X, or Linux.

We plan to support direct printing of trees in a future Mac OS X version of Geom-e-Tree. Likewise, we plan to support exporting of trees as a scalable vector graphic (svg) so that they can be pulled into various drawing programs. If you have a need to do this before this is available in ~2015, drop us a note and we'll see what we can do.

Q: What is the Educational Value of Geom-e-Tree?

A: Good Question.... We think that Geom-e-Tree can stimulate thinking about the structure of the natural world, matter, and the cosmos, but also to a certain extent how geometry and art interact.

Please contact us if there is anything we can add that will make Geom-e-Tree or Twee more valuable in the classroom. Check the explore section of our website for various challenges.

We understand that there is a national effort in the United States to promote the use of fractals in education, and would like to get plugged in to that effort. Can you help?!

Also note that Apple has a 50% discount available for 20 or more copies used in Education. Contact your school's I.T. department?

Q: Is the Angle the number of Degrees between branches?

A: Yes!

Q: What is the Branching Factor or Fan Out?

A: The Branching Factor is simply the number of new branches that emanate from the end of each branch (at a node) as the tree grows.

Q: What is the Common Ratio?

A: The common ratio (CR) determines the length of branches in the tree. The trunk of the tree is divided by the common ratio to get the length of the first branches. The length of those branches are further divided by the common ratio to get the next generation of branches.

The common ratio can be 'strong' such as 2.0 where each successive generation of branches is half as long as the generation closer to the trunk. A CR of 3 (or 1/3) would have the branches getting shorter even faster and diminishing quickly.

The common ratio can be 'weak'. A CR of 1.5 means that the tree branches have a little time to grow but not as long as the 'parent' branch.

A common ratio of 1.0 means basically that ALL branches will be the same length -- even though they are increasing in number at every level . Interestingly, this leads to tiling patterns because you get regular polygons (hexagons, squares) and isometric grids when the common ratio is 1.0.

A common ratio less than 1.0 has the branches getting LONGER in each successive generation -- somewhat abnormal for trees, but this leads to intense overlapping of branches, beautiful tessellations, and very strange patterns.

Q: What is the Perfect Common Ratio?

A: The Perfect Common Ratio is the Goldilocks factor — that is, a reduction factor that is not too little, not too big — it's just right, so that the tips of the branches of the tree come up to each other but do not touch. Benoit Mandelbrot called such trees Self-Touching Trees (cite reference), but we prefer the term Self-Contacting.

Note that you can also make branches overlap by widening the angle so that the branches extend over into neighboring territory, but that is because of the angle, not the common ratio (aka reduction factor).

Q: What does it mean when there is a green border around my tree - around the edges of the display?

This indicates that Geom-e-Tree is in Perfect Common Ratio Mode. (See previous question and answer.) In this mode, the perfect common ratio is computed for you as you vary the angle by panning or single tapping. A double-tap gesture toggles this mode on or off.

Q: How can I tell what the angle is, I mean in degrees?

A: You can always switch to the Share/Save tab. That tells you all about the current Tree.

You can tell what certain 'special' angles are just by looking at the tree. We all know what a 90° angle looks like -- square! Same for 180°. You can eyeball those.

Look at a binary tree with a 60° angle and you'll see that the third branch out on either side is perfectly horizontal. A 120° angle results in those same outer branches being vertical, heading downward.

A 45° angle results in the 4th branch out being horizontal & 8th branch out heading downward. Experiment and satisfy your curiousity. See what 270° looks like. You'll know you are good when you can recognize 72° and 144° angles by patterns they make in some geom-e-trees. 135° is for professionals only. :^)

Q: How can I get the thumbnails in my older arboretum to look as nice as the new thumbnails?

That's easy but may take some time if you have lots, and you want to do them all, and keep them in order. Just start with your first Tree, vivify it, then put that Tree in the Arboretum. Now delete the original. If you go through your arboretum sequentially, the newly created thumbnails will be in the same order as the originals.

You could delete duplicates and weeds before starting. FYI: The new Arboretum will hold 384 geom-e-trees.

Q: Are the trees just stored images that the program plays back?

A: No. Everything you see is computed and drawn in response to your gestures. There are essentially an infinite number of trees that the program can draw because the Common Ratio (above) is a continuous variable. Angles, while continuous in nature, are only adjusted in whole degrees (NOT fractional degrees such as 51° 57' 13''). The number of branches (the branching factor) is likewise integral. So, the combination of angle, the number of branches, and the continuously variable common ratio yields an unlimited variety of trees. Theoretically, every angle could also be divided continuously, but we wanted Geom-e-Tree to work in click-stop degrees so that you could land on every degree precisely with the gestures.

Q: Is Geom-e-Tree 1.3's branching factor limited to 9?

A: Yes.

Q: When I vary the angle of the tree, sometimes some of the branches appear to move up while others seem to move down. Is that a bug?

A: No. That happens as the branches are wound around like a clock. As the tree opens up, the branches on the left move counter-clockwise, the ones on the right move clockwise. They will actually pass each other on their way around if you increase the angle a lot. To help understand this, pay attention to a particular branch as it moves.

Q: What if I have Geom-e-Tree on my iPhone and my iPad?

A: If you have both an iPhone and iPad, the Arboretums are separate. They are backed up with your device, but there is no cross-over or merging of the Arboretums or loss of Geom-e-Trees when you sync your device with iTunes or iCloud.

Q: Can I send a Live tree to another person with Geom-e-Tree?

A: We understand what you are asking. In a future version, we may introduce a URL that describes a given tree. Such a URL could be sent via email, and if the recipient clicked on it Geom-e-Tree would open with that tree in its active space. This would certainly be neater than sending a still snapshot of a tree. It should also be possible to design web pages showing Geom-e-Trees with clickable links that would start that tree on your devices. Is that exciting, or what? (This is essentially what the Arboretum is, a clickable array of tree parameters.)

It would also be cool if people could upload their arboretum to a server where others could view it, or for that matter, send an entire arboretum to another person. Each app could have multiple arboretums to choose from. Maybe we will do these kinds of things someday if enough people are interested.

Q: Where did you get this idea?

A: Please see the History page for that story.

Q: Will there be an Android version of Geom-e-Tree™?

A: Probably someday, after Android tablets (hardware and software) become more standardized. But, we intend to develop the Mac OS X version before Android. It takes time and money to develop an app, and at this time we have little confidence that more that just a few people would pay for any Android version. In the meantime, we assert an exclusive right to port Geom-e-Tree to Android.

BTW, we expect and will discourage knock-offs, such as the totally inferior Fractal Tree app. See A Challenge for Other Developers at the bottom of our Help.

Q: Will there be a Windows version?

A: At this time we have no plans to release Geom-e-Tree or Twee on any Windows device. LoL.

Q: Do you have other ideas for Cool Apps?

A: Yes! This is the first of several apps we hope you will enjoy. Check out PolygonFlux and PolygonTrix!

Q: Where can I send a question or comment?

A: Please feel free to write to TimeHavenMedia @ Thanks again for reading the FAQ, and thinking about these interesting concepts.

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