Taking an Artistic Approach to Math

Taking an Artistic Approach to Math

Working to sort through the 240 unique solutions of the SOMA puzzle.  My theory is an elaboration of work by others that is is summarized nicely in the last paragraph here:
https://en.wikipedia.org/wiki/Soma_cube.

My method is to treat the problem as "not a problem."  The SOMA cube pieces are beautiful objects so why not make many of them and treat them as a the medium for math based sculpture.  I discovered that 1" x 12" x 48" pine board  rips and cross cuts into lots of 3/4" cubes.  The cubes are glue into the seven SOMA pieces and then colored with food coloring.


With lots of cubes visualizing the variety of solutions that can grow.


I worked through the 42 seedlings and discovered that I was coming up with more than 240 solutions. Reviewing previous work on sorted solutions:
www.fam-bundgaard.dk/SOMA/NEWS/N151008.HTM
I discovered that 42 is not (this time) the answer to the life the universe  . . . everything

Interesting patterns emerge nonetheless showing the similarities of many solutions.

I think this one is particularly beautiful growing from what I originally considered to be Branch 4.
I call it "Triplets Two Twins and Twisted Sister."

Friends playing a shape building guessing game similar to pictionary:

RAIN On Your Brain With the Rainbow While Driving

This is a little something to try while driving to keep your attention on the road and deal with stressful traffic. It is based on R.A.I.N. (Recognize, Accept, Investigate, Non-identify) a mindfulness tool for dealing with strong emotions.  A good explanation of it can be found here:
http://tarabrach.com/articles/RAIN-WorkingWithDifficulties.html

The idea here is to look for each the colors of the rainbow and go through the process of RAIN for each one.  For instance:

Recognize Red - Red is the next big thing.  Hey, Red 'sup?

Accept Red - Red is in the house! Yo, Red thanks for being in my head!

Investigate Red -  Where is Red? Taillights, Red cars, stop signs, stop lights, lots of stuff is Red.  Move your head around, look left, right, further up the road, check you r mirrors.  You are supposed to be doing this stuff anyway.

Non-Identify Red - Later Red! Letting go. Detach. Red happened and now Red is done.

Do the same for Orange, Yellow, Green, Blue, Indigo, Violet.


OK, Indigo and Violet are not always jumping out at you when you drive.  Just do Red, Blue, Green a few times in a row.  The idea is to use the commute as a mindfulness tool not subscribe to a rigid structure.  


When I go through the rainbow at a relaxed pace set by inhaling and exhaling deeply two or three times for each step it takes about 15 to 20 minutes.  That is pretty decent amount of time to spend in a mindful way and I get to do it while I am driving to work.  

11 NOR Gate Ring Oscillator

More Christmas lights.  My day job is doing the plant shutdown thing through Jan. 2 so I am planning to get 36 gates onto this board and route a 3 bit up counter.  At least something with two clocked D Latches and logic.

What The Heck Is That Thing?

Well, get a picture of me standing next to it. . .

How handy is that?  I can post a YouTube video directly to a blog post.  The blurriness of the opening shot appeals to me in some "what the heck is that thing?" fashion.  This is the first video I shot and posted of the NOR gates in action.  In this instance as a simple ring oscillator.

NOR Gates

Getting Started On The Large(ish) Array

Started to build the latest iteration which should allow for 51 NOR circuits.  Maybe less, no point in crowding parts and making it hard to solder.

Here I am moving along to make sure I can fit three rows (two down one to go) before I start building across the protoboard.  The 110 VAC thing is a bit worrisome but I am disciplined about when to power up and test.  The complete assembly will be properly cased to prevent any inadvertent contact with dangerous voltages.

I think I should have enough NOR gates to do a 3 bit up counter.  Here is my latest least number of NOR gates edge triggered D Latch:

The lower circuit is the actual D latch and the upper circuit is "pulse shaper" which conditions the clock to be of short duration.  The pulse shaper should only be required for every four latches which should save on NOR gates.  I am thinking a 3 bit up counter would take about 35 NOR gates.  I will draw one up in the next few days as build and test circuits on the protoboard.  Maybe have something running this weekend.  I should do a video of the edge triggered D latch at least by this weekend.

Cellular Automata Or Something Else?

I put together a "ring" of D Flip Flops with the data input set by XORing nearest neighbors, which seems to me to meet a version of the "Conway's Game of Life" rules:
1. Too many neighbors = off.  In this instance too many neighbors is 2, one on each side
2. No neighbors = off. I this instance no neighbors is no one on either side.
3. Just right = on. One neighbor on either side.

Below is a screen shot of the circuit, including a simple preset and the results of manually clocking through 7 states.  It appears to begin repeating at state 4.

If you are interested in designing a simulating digital logic I highly recommend "Cedar Logic Simulator."
You can get it here for free:
http://sourceforge.net/projects/cedarlogic/

The next step is to do the same thing but with all NOR gates.

Planning for Publication

1. Read "Incredibly Useful Advice for Physics Students Writing a Senior Thesis."  This is a perfect application for the netbook.  Kinda the whole reason you bought it.
2. Use the blog to collect your thoughts and codify your effort.  Conceive, Believe, Achieve are more than just words.  It has worked before and it will work again.  Particularly for  a goal that lends itself to being split into "doable chunks."
3. Collect references for the bibliography and comment on them.
4. Construct an outline and or table of contents for (Working Title) "Cellular Automata Using Optically Routed NOR Gates."
     a. Purpose - Demonstrate a technology for implementing sequential and combinatorial logic circuits from novel components that are comprehensible to an early engineering education audience.  Including how to construct a simulation program.
     b. Survey of previous work by others
     c. My work to present date
     d. How it works in hardware.
     e. Example circuits leading to and including CA
     f. Utilizing MIT open course resources to suggest a curriculum for a hands on digital logic and elementary computer science class for pre college students.
     g. Conclusions
     h. Acknowledgments
     i.  Bibliography
5. Overcome reticence in taking next steps.  The secret to edge triggering sequential circuits was in your previous research from 1995.  What you did and can do takes precedence over what you read and what people tell you is possible.  (I am generalizing something that happened to me in second person voice, hmmmmm).  Oh, well.
6. Query the SPIE conference representatives?  I think that was how I got started last time.  A mentor or collaborator would be nice.
7. Build the the 51 NOR gate board.
8. Simulate 1D CA in Cedar.
9. Work on simulator in Scheme.