Rotating Hexagons

This is a p5.js script I started played with as I get ready to post about stop animation in my 52 weeks of hands-on-math. Here is a link to edit code. You may want to play with the angles, number of sides in the polygon, rotation rate, etc.

If the javascript isn’t loading, then here is a movie:


I used the polygon function from this website: It references this series of videos to make generative art:

Sticky Note Sunflower

What you are seeing is a growth pattern of sticky notes that uses the Golden Angle (137.5 degrees) and then slowly decreases. This angle is commonly found in the plants all around us because it is an optimal angle for growth.

It was a lot of fun playing with the growth angle while creating memorizing spirals in this code, so I created a version for everyone to play with (see below): (on p5.js – sometimes this network goes down) or:

See the Pen sunflower by Sophia (@fractalkitty) on CodePen.

There is lots of fun to discover here. The fractal starts using the Golden Angle of Phi (137.5) and then decreases. You will find interesting behaviors when the angles approach numbers that divide into multiples of 360 more easily (40, 45, 60, 90, 120, 180, etc…). I wanted to do so much more, but had to stop somewhere.

If you want to know more about Phi, many mathematicians and creative types have presented it better than I (see below):

I’m Attracted to Attractors

So many plots and mathematical musings throughout my life have brought on a sense of artistic beauty and awe within my being. In the windowless halls of engineering firms I have smiled at harmonics, or in a homeschooling room squealed in glee when I stumbled upon Pisano periods by trying to play Fibonacci on the piano. Lately I have been playing with attractors. These dynamic systems make me stay up late fiddling with their metamorphic and chaotic beauty.

I came from a Matlab world and have had to teach myself some more cost efficient means of play with javascript and python. The code below is just one of my playgrounds. I don’t know if there is a name for this attractor (please let me know if you know its name). Enjoy:


With functions you have inputs (x) and outputs (y) that can be plotted on a plane (x,y). With the images below, the x and y values are computed using an initial value of (1,1) and then the next (x,y) is computed using the previous coordinate’s values. The equations are shown below:

x = sin(a1 * oldx) * cos(a1 * oldy) – sin(a2 * oldx);
y = cos(a3 * oldx) – cos(a3 * oldx) * sin(a4 * oldy);

Here is a gallery of some of my outputs:

For the images above, I calculated x and y using a1, a2, a3 and a4 coefficients and the previous x and y values (oldx, oldy). The initial point was (1,1). In the code below, there are only 300,000 points (compared to millions in higher res images). You can play with the values of a1, a2, a3, and a4.

See the Pen webcode by Sophia (@fractalkitty) on CodePen.

I like the p5.js editor. Click here to play. I would say that fiddling with this is a great idea for an “Hour of Code.”

If you like to play with sheets or excel, which is not near as pretty, I made a sheet for you here. This is also handy if you want to see the array of values for (x,y).

Have you Tessellated today? Rotational Play

I posted on translating tessellations yesterday, and ended up playing with a rotational tessellation on my ipad. I had to laser print it of course and see all the various patterns. I love math!

If you want the svg file, I have it on my Etsy for $1.20 here.

Aliens, Planets and Nebulae Update:

Mission 5 is now posted to the Math RPG page. I know I say Math RPG, but we all know that this is a total STEAM game. I can’t believe some of the absolutely creative and innovative ideas students come up with. Music blasters, laser cutters, lego models of carnivorous sunflowers, pages of comics about the crew, and so on.

I hope to have all 10 missions up and posted in the next few weeks. I feel that once 10 missions are posted, facilitators will be comfortable enough to create their own for the topics they would like to cover. Please send any feedback and if you haven’t checked out the game yet – here is a link.

Do we want to create a mission folder where facilitator can share missions? Let me know. I would love to see this project based learning while in character grow.

KMUZ Poetry on the Air With the Family

KMUZ’s Steven Slemenda interviewed our family in a two part series for a wonderful program called Poetry on the Air. Thanks to KMUZ and Steve Slemenda for sharing. This show is in the archives on their website, and with permission I am posting it here. My children were appreciative of the experience for the interview. It was such a wonderful exercise for them to reflect on. We are grateful for a way for voices to be heard in our Salem Community.

8-20-19: Interview with Sophia’s Children
9-13-19: Interview with Sophia