SketchUp is a free and fun program for 3D modeling. You can use SketchUp to design just about anything, from furniture to a dream bedroom to an entire city.

There is a downloadable version called SketchUp Make, which you can get here. But there is also a web-based version which works right in your Internet browser. This version is called my.sketchup, and to use it just go to www.my.sketchup.com.

In the previous SketchUp project, we created a Fibonacci spiral:

In this project, we’ll use this spiral to create flowers.

If you created your own spiral and saved it, here’s how to get it back:

Open my.sketchup. Click the Folder icon at the top left corner and choose Open.

Browse to the spiral model you saved, and open it.

If you didn’t create your own spiral before, never fear – you can download one. Here’s how:

Open my.sketchup.

We don’t need Josh in the model, so press E for the eraser, and click on any of Josh’s edges.

To use the spiral, we want to start in Plan view (also known as top view or bird’s eye view). Click the Views icon on the right side.

In the Views window, click the Top view icon.

Now we’re looking straight down at the “ground.”

To find the spiral model to bring in, click the Components icon on the right side.

In the search field at the top, enter “fibonacci spiral.” There will be several results, but the one we want to use is this one, by Bonnie Roskes. Click this thumbnail, then click anywhere in the model to bring it in.

Anything brought into SketchUp this way comes in as a component – a single object comprised of faces or edges. We don’t want this spiral to remain as a component, so right-click on it and choose Explode.

Once exploded, the spiral is broken down into a new set of smaller components. While all of these are still selected, right-click on any edge and choose Explode again.

Now there are no more components, just one long curve. Leave it selected.

Activate the Rotate tool (press Q), and click to place the protractor at the inner endpoint of the spiral. You’ll have to zoom in very closely to click this point.

Press the Ctrl key (PC) or Option key (Mac) to make copies. You don’t have to keep this key pressed, just tap it to make the “plus” sign appear. The next two clicks define the rotation angle – click anywhere to start, then move your mouse and click again when the Angle field indicates a 45-degree angle. (If you can’t get 45 to appear, just type 45 and press Enter.)

Immediately after that first copy is created, type 7x and press Enter. (Remember, you never have to click in the field that currently reads Angle – just type and the numbers appear.) Be patient if SketchUp needs a few seconds to complete this. Now we have seven copies, or eight total spirals.

The trick to making the flower is taking the eight spirals we have and making a mirrored copy of them. We’ll start by making a copy in blank space. Select everything again (Ctrl + A), and activate the Move tool (press M).

Tap the Ctrl or Option key again to make a copy, and click two points so that a copy is placed anywhere in blank space.

Now the copied spirals should be the ones selected.

With the copied spirals selected, press the S key to activate the Scale tool. A set of eight drag handles now surrounds the spirals.

Click the handle at the center of the left side, and move it to the right so that the spirals turn inside-out. Click to finish when the Red Scale value is -1, or just type -1 and press Enter. Again, leave these spirals selected.

Zoom in very closely at the center of the selected spirals and activate the Move tool again. Click the center of the selected spirals.

For the second move point, zoom out then in again, in order to click the center of the original set of spirals.

Zoom out, and this is what you should have:

To break up all of the curves where they intersect other curves, select everything, right-click on any selected curve, and choose Intersect Faces / With Model.

Use the Eraser to remove the partial curves around the outer edges.

Now comes the fun (colorful) part. We’ll create one set of spiral faces first, then make rotated copies of those faces to complete the first flower.

Activate the Line tool (L) and click any two adjacent endpoints within the edge shown below.

This fills in faces on either side of the traced edge.

Continue tracing small lines along every other edge, working from outside to inside. When finished, you should have one complete spiral filled in.

To paint these faces, first click the Materials icon on the right side.

Click the Browse icon at the top right, then open the Colors collection:

In this example, the six rainbow colors are used in a repeating pattern.

To copy this painted spiral, select everything again. (This selects edges as well as faces, but it doesn’t matter if edges are copied on top of existing edges.) Activate Rotate, and place the protractor at the center of the spirals.

Press Ctrl or Option, and click any two adjacent, similar points around the flower. The angle, as when you created the rotated set of spirals, should be 45 degrees.

Enter 7x, and the faces are copied. (This is a resource-heavy operation, so don’t be surprised if SketchUp takes a few minutes to complete it.)

Try This!

You can create flowers using different rotation angles and color schemes. For example, if your Fibonacci spiral is rotate-copied using an angle of 30 degrees with 11 copies, you can get something like this:

For an even more detailed flower, this example uses a rotation angle of 12 degrees and 29 copies. It took quite a while for SketchUp to complete the rotated copies.

Learn More

Sunflower

https://www.popmath.org.uk/rpamaths/rpampages/sunflower.html

Scratch projects

https://scratch.mit.edu/projects/168404566/editor/

Fibonacci Flowers in Scratch

https://video.search.yahoo.com/yhs/search?fr=yhs-Lkry-SF01&hsimp=yhs-SF01&hspart=Lkry&p=fibonacci+flowers+in+scratch+youtube#id=15&vid=9a36f541c7b9b58b63ac1f07a886907c&action=view