What's a geom-e-tree?

From its trunk up through its branches, a geom-e-tree (or Tree) is a geometric figure that has the same structure repeated throughout:

• Starting from its trunk, a geom-e-tree has the same number of branches at every node. This is the Tree's branching factor.

• Branches at each node are separated by the same angle.

• The lengths of branches vary from one level to the next according to a common ratio.

Trees have many surprises! Geom-e-Tree 1.3, The App, provides an entertaining, educational, immersive experience of geom-e-trees. We invite you to relax and enjoy all the brain-stimulating patterns Geom-e-Tree has to offer.

What's New

Version 1.3

Geom-e-Tree has some really wild new themes to chose from!

We've made the branching factor easier to change — A two-finger tap in the upper or lower half of the display increases or decreases the number of branches at each node in the Tree.

The double-tap gesture now toggles the Perfect Common Ratio Mode on or off.

Significant Improvements:

• A Two-finger tap was introduced as the gesture for changing the branching factor up and down. The previous multiple-finger taps are no longer recognized. The new gesture makes it easy to see the effect of changing n while holding the angle and common ratio the same. (The kids' app, Geom-e-Twee, still uses just two or three fingers to directly set the number of branches to two or three.)

• We increased the maximum number of Tree branches to nine. The new gesture for changing the branching factor made it easy for us to allow 8 and 9 branched trees. Previously, a five-finger tap limited the number via gestures. We had 7 and 8-branched Reference trees in the arboretum that could be used to get a Tree of those degrees, but that was a hack.

• The double-tap gesture now toggles the Perfect Common Ratio Mode on or off. A narrow green border is displayed when a Tree is in PCR Mode.

• We added not just new themes, but new /kinds/ of themes: themes that vary line width as well as line length, themes that draw 1000's of dots at the nodes of the Tree instead of drawing branches, themes that draw nodes and branches, themes that draw nodes that vary in size, themes that draw circles at the midpoints of invisible branches, plus several other kinds of themes!

Minor changes and bug fixes:

• Tree line widths now appear (relatively) the same on all devices, and in thumbnail images, email messages, and photos. Previously, lines were not scaled consistently based on the image size. Dots (new in this version) are also scaled to match the image size.

• A red border previously was indicated when the common ratio was being constrained. Now, red prohibition signs appear in both upper corners.

• We tweaked the Rainbow theme colors, rounded the end caps, and changed the light blue background to neutral gray.  We added pivot rivets to the Pop Stick theme.

• The Arboretum was enlarged to hold 384 Trees.

• We updated our code for iOS 6 and retina devices, and improved performance.

• When sending a Tree in Email, the attachment is given a useful name. For example "2-180-1.618.jpg" means it was a 2-branched (binary) tree at 180° with common ratio 1.618.

• Geom-e-Tree's Help and were updated to reflect changes, and to give you better information.

Ratings and Reviews

4.6 out of 5

9 Ratings
9 Ratings

Nice app, fun, interesting, could be updated


I have many of the fractal apps, and other “geometry” based art creators. This one is different than most because it constrains the angle and common ratio. This forces very nice geometric shapes. While you can create trees, you also can create other structures. On an iPhone 6 the resolution is very good and it redraws essentially instantly. So, very reactive and easy to use. There are several starting points where some constraints and colors are set, and then you can create from there and save. The trees that are for kids are particularly nice to start with, very colorful.

The reason for the minus 1 star is that the save to photo feature will not scale to the aspect of the screen (it actually has a feature to scale, but at least for me, as soon as you pinch-zoom, it snaps back to its default setting) - as a result, for example, you cannot save to wallpaper easily, it requires editing. I use these art creators to make backgrounds for my phone.

Excellent app, and fun to use.

Good times for me, friends, and kids

Maria Droujkova

I keep Geom-e-Tree in my small folder of toys "for when I need calm and comfort." I have been playing with it for more than a year now - when I am waiting, when I want a few minutes of beauty in my life, or when I want to create an example of a fractal for illustrating something.
I also share it with friends as an example of accessible, deep math toy. It's a good conversation piece!
And finally, kids. It works great as a smart toy that delights, occupies, and teaches kids - as young as toddlers, and all the way to teens. When we meet with other parents, I often give my phone with Geom-e-Tree to their kids to explore. It's very engaging.

This app is beautiful.


I am very grateful that this has been release in this format.
This is geometry made fun and easy,
One feature that could be useful is in addition to the intuitional controls a more refined/defined interface of adjusting angles and lengths. I find when pinching to make a design more complex it can be hard to get just the right length for the image I am wishing to create. Also as the geometry gets more complicated the app tends to slow way down, I feel as if this might be able to be fixed with newer generation iPads/iPhones.
More starter trees/images could be cool as well or perhaps access to a sharing of images others have created.

This is wonderful work. Thank you, I look forward to other future apps and upgrades.


2.7 MB
Requires iOS 5.1 or later. Compatible with iPhone, iPad, and iPod touch.
Age Rating
Rated 4+
© 2013, John E. Miller -- All Rights Reserved.


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