More spirals

Here’s another animation of the sunflower phyllotaxis pattern (an example of Fibonacci phyllotaxis). Florets/dots are sized relative to distance from the center, and fade from white to black and back again, also at a rate based on distance from the center. (See previous post here.)

(Click on image above to view video.)

Dragging directly on the movie playback nub let’s you see the video faster, which makes some of the slower patterns more apparent.

All this inspiration owed to one KrazyDad blog post.

June 28, 2007. patterns. No Comments.


I have to admit I’ve dumped numerous hours into facebooking the past couple of weeks. Brent invited me to join right before I went to Texas, and I resisted for a few days, but thought I’d try it out. And now I am somewhat hooked. I have connected with old elementary school friends, seen pictures of people I haven’t thought about since college, and best of all, now have a new news feed: What is happening in the world of people I actually know.

Today’s news includes:

Here are reasons I like facebook:

June 27, 2007. computers/programming, friends. 3 Comments.

Why I can’t stop eating cherries

Because these two things are true:

Food by induction!

June 27, 2007. food. 1 Comment.

Fermat’s spiral

Whoa, holy crap. I sat down to try to understand Fermat’s spiral a little bit better last night, and I ended up with a pretty cool animation.

I started with the Wikipedia page, and there I saw this image, with the following caption:

sunflower spiral

The pattern of florets [say, of a sunflower], produced by Vogel’s model, (central image). The other two images show the patterns for slightly different values of the angle.

Those “other two images” had me wondering… for what different values of the angle? I wanted to see what the curve would look like with different angles (see the equations provided on that page), so I wrote a little script with my new favorite programming package, pygame, creating one big loop from 0° to 360°. Some very interesting patterns result!

(Click on image above to view video. It may take a few minutes to load, depending on your connection speed. A much smaller video is available here.)

The only thing changing here is the angle in the second equation (top left of video). c is just a constant to stretch things out whatever amount, and n is all the integers from 1 to 140 (so we get 140 dots per changing angle = 140 dots in every video frame). r is the radius of each dot from the faint gray dot in the center of the window, and Θ is the angle of each dot’s location, with 0° straight right up. At 137.5° (the golden angle), you see a tight packing of dots that is just like the arrangement of flowers/florets in a sunflower.

When do you think the pattern will repeat?

Addendum/Correction: Since I originally posted this, I rewrote the code in Processing, and discovered that I had an error that is evident in the movie in this post. I don’t know why I didn’t notice it before. You can see the error kick in around when Θ = n x 37° … More and more dots show up in the wrong position, soon after resulting in some major weirdo non-spiral action (as is clearly evident at, for example, 44.4°). This error is the result of me treating radian values as if they are values in degrees. Dammit, if this doesn’t catch me again!

Still looks neat, though. ^_^

June 25, 2007. computers/programming, patterns. 3 Comments.

How much do I move when I sleep?

For my final project for sensors class, I wore accelerometers on my head, arm, and leg for a full night’s sleep, and tried to track how much I moved during the night, and which positions I tend to sleep in.


Main findings:

I wrote up some quick notes about the project here.

June 14, 2007. academics, information visualization, media lab. 1 Comment.

Mmmmicro sundae

I had a “micro sundae” for the first time at Toscanini’s yesterday. [Man, the number of times I write about that place, you'd think I go there every day or something... :)]

A micro sundae is a mini-scoop of any flavor ice cream you like, squished into an espresso cup (or a Dixie cup, if it’s To Go), then covered with hot fudge, then real, sweetened whipped cream (the beige, clumpy kind).

I had mine with cookies and cream ice cream.

I was “without camera” at the time, so here are my flickr findings on Toscanini’s micro sundaes (thank you, mossybaby and chessie monks!):

micro sundae creepy micro sundae 1 creepy micro sundae 2

I think I’d prefer a micro sundae from Tosci’s to a Serendipity Golden Opulence Sundae any day.

June 14, 2007. Boston/Cambridge, food. No Comments.


I’m in Austin, land of huge grocery stores, and yesterday I was in the local H-E-B with my dad and sister. In the produce section, I noticed these:


My dad explained that they were a mix of apples and grapes, that resulted in “an apple… that tastes like a grape”. But I picked them up to have a closer look… They were normal Fuji apples, and they smelled distinctly like artificial grape flavor (just like grape soda). We were both slightly horrified at the smell, and were wondering how they are made. The Grapple website (nice site!!) provides little information:

How Is A Grāpple® Brand Apple Made?

Grāpple® brand apples begin as Washington Extra Fancy Fuji Apples. Of all apples this is the one that takes on the grape flavor best.
This Patent Pending process is complex and the ingredient mix primarily includes concentrated grape flavor and pure water. All ingredients are USDA and FDA approved and the process has been licensed by the Washington State Department of Agriculture.

There is nothing but flavor being infused into the Fuji apple. The apple takes on no additional sugars or calories. They are not genetically altered in any way.
The apple is as healthy as ever but now has the new exciting grape flavor.

The Wikipedia says that they are Fuji apples soaked in artificial grape flavoring.

It’s a little scary that we feel we have to make our juicy sweet apples more appealing to kids by making them taste and smell like grape flavoring.

June 5, 2007. family, food. 1 Comment.