Floating Code

All that remained to complete the geodesic dinghy was to secure some hardware, primarily the oarlocks’ side mounts, and a paint job.


Because the boat is viewed in an experimental light as a prototype, I avoided height-priced marine paint in favor of Valspar’s extreme weather primer/paint (fog gray) on top of the fiberglass brushed onto the plywood hull’s outer planes. The deep blue inner planes were set off by white structural members to accent the skeletal geometry.

Getting it to the water was the next big challenge. To meet it, two 2” x 4” racks were built to set on the top of a Jeep Cherokee. My brother and I then carried the boat’s nearly 100 pounds almost a hundred feet like a large sofa around a variety of obstacles. Once in position, my next worry was allowing all the boat’s weight to rest temporarily on its stern edge before tilting onto the back of the jeep. But it stood, and with the additional help of my technical advisor, we 3 wrestled the boat into position upside down on top of the Jeep for about a half hour. Once lashed down with the bow to the front, the boat fit the angles of the Jeep like it belonged there. Even so, the 12 mile trip to the water was driven slowly, going 35 mph in a 55 mph speed zone to the landing area characterized by lumps of sand covered with ice-plant.

With the boat intact at the water’s edge, my biggest concern was the obvious: would it float –without leaks. The layer of fiberglass that I coated the plywood with was stretched thin due to the misfortune of having to make do with left-over hardener because someone had lifted the one that was supposed to be included with the newest can of resin I had just purchased. But after securing a line to the boat’s twin bow eyes and pushing it off, it not only floated but did so beautifully. From one perspective, the gap between the side panels and the waterline created an infinity pool-like illusion of being suspended on a layer of air over the glassy water’s surface.


The next test was to get into the boat, push off and see if everything held. For the next few minutes, I inspected every panel and seam more than half expecting a small breach somewhere, but not a drop!

With this crucial test passed, the next test was to determine how effectively the boat moved with temporary makeshift oars. My chief concern was the oarlock positioning, and I soon discovered that, while not perfect, the boat was both easily propelled straight in a desired direction and turned to another with the boat’s simple geometry having just enough complexity to supply a plane angled to allow a path for water to get out of the way.


During these initial tests, my technical advisor and I recorded measurements of how the bow and stern sat in the water. Of course the next worry was to see what happened with a passenger sitting on the stern seat. I had made a rough estimate that the volume of the water displaced by the weight of the boat and 2 people would equate to the bottom edge of the side panels. This turned out to be close on the average (about an inch above the bottom edge), but the boat was naturally tilted to where there was only 5-6” of freeboard above the lowest point of the stern region. Even so, water was not gushing into the boat, but I wouldn’t want to tempt the situation in anything but mellow seas. The important thing with 2 people in the boat was that it still didn’t leak.

The waterline readings and the rowing test results told me that the rowing seat and the oar locks should be shifted about 4-6” and 2-4” forward respectively.


I would also increase the contribution of the hexagonal expansion of the central section about 2-4”, and decrease the stern section dip from 4” to about 2 ½ – 3”. Beyond this, a healthier layer of fiberglass would make for more worry free use and extreme weather paint for the inside also be much better.


All in all I am generally satisfied with the outcome. Some future testing remains: A receding tide prevented determination of how well the boat rowed with a passenger. Aside from this, I am looking forward to what it is like to camp in the boat at anchor and transporting a bicycle on a yet-to-be constructed rack.

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Geodesic Dinghy

An idea for a small code-guided boat I had dreamt up and put aside for a possible future recently found development opportunity with the coincidence of time, place, and tools to at least build a prototype.

As first conceptualized, the vessel’s intended function would be to transport needful things between the shore and a hypothetical larger live-aboard boat moored nearby or perhaps as far as a day and a half’s rowing distance away. More specifically, it would have to be capable of carrying a week’s supply of fresh water and groceries, laundry, garbage and sewage, a 20 lb. propane tank, camping gear, and a bicycle – or a passenger.

To design such a dinghy, the code’s transport template was drawn upon with heavy reliance on the hexagonal expansion (HXP) comprised of alternating triangular prism geometry.


Although such an application rendered the term geodesic inaccurate in relation it’s technical and popular (dome) meanings, the departure might be reconciled by viewing 2 lines of continuous sphere centers, around which the boat is structured with bode geometry on either side of the flat HXP “keel” – with those lines pointed in the direction of motion.


Because the boat would be operating in very shallow water over flat muddy bottoms, I decided to employ the template’s triangle down option with its relatively flattish (19°) chines. For overall size, a simple 8’ long by 4’ wide by 2’ high (at the highest point) was sought. An HXP seating structure draws upon bode geometry angles for bracing, is one foot high for stowage, and is broken up aft of the rowing seat for ease of boarding.


Because the contours of the triangle-down geometry dipped at bow and stern, the former will be covered to guard against splash, and the latter raised for passenger safety and comfort.

For the boat’s skeleton, I used 2×2’s and 2x3s, ripping them at angles that split the total dihedrals between intersecting planes (of which there were 5). In striving for economy of material and cuts, I tried to rip each piece in half for use on either side of the boat but neglected to account for the saw blade width which is significant at these scales.


This mistake, plus the lumber’s non-perfection, the old ripper’s lack of precision, and an inexperienced operator resulted in a lot of slop. Miraculously however, it all came together. Seated on the stern above is the monarch who has been overseeing the project from her bathroom.

Much of the slop seemed to be absorbed by the rectangles which degenerated into parallelogram. This made jig sawing, ripping, and grinding the plywood sheathing – ½” for the bottom and 3/8” elsewhere – a laborious process, but again it all came together with 1” deck screws. Seams varied from zero to ¼” gaps and were filled with fiberglass resin before laying 4” wide matting into swaths of same. It is inspected below by the old salt who is my technical advisor.


Thus are the critical phases of the project essentially completed. Painting, specialized hardware, and details remain. The next post will recount these along with initial testing to determine if the dinghy actually floats, rows, and bears loads. So far, the project has taken 3 times longer than originally estimated. Because I give myself B+ for design and a D- for craftsmanship, how well the boat will actually do is a mystery at this juncture.


Posted in Code Application, Rolling Transport, Wheel Extrapolations | 1 Comment

Making a Stand for Homegrown Energy

The availability of inexpensive portable-scale solar panels, batteries, and chargers makes building a structure to support them a worthwhile project. For less than $20 and a couple of spare hours, just about anyone with a small space exposed to a few hours of sun should be able to build their own customized stand to meet some of their electricity needs.

solar-stand-lumber-cutTo make the stand suitable for a particular location, (celestial) cube-based geometry is engaged and the following poses an example of how mine came out. To support would might be characterized as a doll house-sized “roof”, I took a piece of 2” X 8” lumber and chop-sawed it at the angle of my latitude (35°). In making this cut, I could use both sides for the base.

On top of the 2” thick edge, I nailed a 1” X 8” board to accommodate the panel. That is all there is to the stand’s structure which is quite easily moved to and away from a sunny spot facing solar noon for a few hours. Other considerations remain. To harmonize the base structure with its surroundings, I took the safe approach and simply followed the home’s 2-tone color scheme to make it seem like a part of it. For those who possess an advanced artistic sense, a color scheme might be chosen to distinguish the stand in a complementary way.


But paint is more than just for aesthetics. For the top sun-facing surface around the panel, a color selection is required to counter the ill effects of the low albedo panel because, truthfully, its blackness absorbs (and re-radiates) sunlight just as the much if not more than the popularly demonized carbon dioxide molecule. Luckily the antidote for this is to simply paint the surface around the panel with a high albedo hue to reflect light right back to space.


Generally speaking, the default color choice for this is (glossy) white. By painting an area white equal to that of the panel, the overall albedo of the stand’s “roof” is increased. This translates to both global and local cooling effects. Regarding the latter, I can confirm a quite a noticeable difference when handling the panel after several hours of exposure. The cooling effect around the panel also makes it run more efficiently. One can fine tune the albedo factor by proportioning exposed area to a desired ratio and/or by tinting the white with softer colors and/or creating a pattern to make the panel less conspicuous and imposing.

My half square foot, 6 watt panel with the corner ear loops cost $50 and the 5000 mAh battery is sufficient to handle my personal lighting needs, as well as being able to charge an AA/AAA battery charger to run other items like bike lights, an mp3 player/radio, and a computer mouse.

All energy sources have their positives and negatives and I believe it is fitting and wise to match each type to its use. In my view, the direct semi-conducting driven process of photo-voltaics should be applied to semiconductor devices – LEDs, computers, TVs, stereos, etc. To do so would take care of a significant chunk of the electricity usage spectrum.

Posted in Code Application, Contemporary Relevance, Cube-based Shelter | Tagged , , | Leave a comment

Bode Wave Development

Thus far, primary elements of bode geometry – point spheres, line edges, and dueling planes (squares and triangles) – have shown they can, by their characteristic arrangements and interplays, readily generate other forms.

For instance, in addition to the intrinsic axes ascribed to any of the bode’s 6 radial line sets, 3 alternative axis types are easily derived from opposing sets of squares, triangles, and edges by reason of their having easily determinable midpoints which are in line with the bode’s center-points. From these, can naturally be generated – with their slopes shaped by the angles of elements spun about, and relative to, the axis employed.

Cuboctahedron Sections

Once cones are generated, parabolas, ellipses, and hyperbolas are created by sectioning the cones with planes intrinsic to the bode. Ellipses are actually sectioned more directly from planes intrinsic to the bode’s intrinsic spheres, which brings me to the crux of this post: Is there something intrinsic to bode geometry that leads to, or naturally expresses waveforms?

Cuboctahedron Wave PrismWhen waves were first applied to the mounds, berms, and architectural embankments of ground design, no explanation was forthcoming of anything bode intrinsic because, frankly I hadn’t given the matter much thought. All that was stated was something to the effect that the wave represented the most elegant transition from one level to another. Bode geometry only came into play to specify a wave’s maximum slope using the analogy of a prism splitting random terrain (white light) into a quantized set of waveforms. Although this might represent a novel application, the wave itself appears to come from outside the realm of the bode.

But if conic sections can be derived so easily, it would seem waves should also, especially in light of the bode’s intrinsic rotational dynamism, and by the notion of the sphere being sectioned more directly than the cone to create an ellipse.

By such considerations, the following constitutes a hodge-podge of observations and musings, beginning with the sectioned circle; its rotation via the preceding rationale; the mathematical and possibly natural relation between it and the wave. By this I refer to the sectioned bode circle in a square context. Pictured thus, relative rotation is only observed by focusing on a point of the circle’s circumference, with such a point being relational – as opposed to the circle’s integral center-point. In this context, “relational” manifests explicitly in terms of other spheres or, in this case, between one sphere and the square.

Cuboctahedron Wave Generation

Between the sphere and the square, the relational contact points define the 2 axes of an X,Y plane such that the position of a rotated point can be described separately in 2 dimensions of the square grid’s orthogonal lines. When the ratio of the point’s horizontal and vertical distances to the radius changes via rotation keyed to the arc length subtended, the plot of the relation is a wave. Does this mean waves are derived from bode geometry as the conic sections are?

Relative rotation of the sectioned (sphere) circle in the square grid context. Does nature care about such ratios? Perhaps only if the ratios are parameterized with time inferred by rotation.

What about the circle’s relational points? When the parallel (square) planes of the celestial co-cubes are rotated relative to each other, so go the relational contact points and their wave-manifested ratios, a happenstance that lends CBA yet another dimension of expression. Although this wave connection is somewhat compelling, the relation to bode geometry is not immediate.

Circle Wave Relationships

With the rolling wheel, on the other hand, the cycloid of one revolution equals one wavelength of the rotated circle. However, there is still no specific bode association, let alone a unique one. The superimposed square to triangle transformation arcs supply an alternative mechanism for rotation, but does this translate to a generated wave? Length of the arc comes into focus with π, but there is still no intrinsic bode distance between spheres that involve that constant. How about rotation of the triangle about the common edge to superimpose itself on the square?

In the model of electro-dynamic behavior posed by bode geometry, triangles oscillating on either side of a propagating line reflect the mutually orthogonal electric and magnetic fields embedded in the bodally arranged octahedral spheres. Alternatively, the shortest line distance between vertically aligned points of the triangle-up bode looks like it could correspond to a matter wave. If either or both of these present a sound correlating picture of EM and/or gravitational behavior, the bode can be said to possess the wave intrinsically. After all, alternators are circularly rotating devices with no apparent wave connection, but that is exactly what they make.

Cuboctahedron Matter and Electromagnetic Waves

I am skeptical. It seems more likely that the bode pattern infinitely generated poses a good representation of the space-time fabric through which waves travel. I.E., waves are not something in the bode that can be evoked and brought to life, but are caused by a disturbance, be they electrons, winds blowing across the water, or a meteor crashing into our plastic crust.

One last matter: In formulating the wave mathematically, the maximum slope and the radius of the generating circle from which the ratios are described occupy the same place in the equation. What connections can be made, especially in the context of bode geometry?

Circle Radius-Wave Slope Relationship

For one, spheres may seek to touch diagonally across the square by enlarging their radii, with a similar situation found in the triangular cluster. Radii also undergo a change with formation of the ellipse as a rotated sectioned sphere circle, with the circle’s relational points becoming foci. Relational contact points of other spheres angled away from the reference unity sphere poses another scenario. Otherwise, something akin to shoaling relates size and slope as a wave is created or transmitted through the faceted bodal prism.

Posted in Code History, Cube-based Shelter, Derivations, Extra-topographic Guidelines, Ground Rules, Polytechnic Integration, Rolling Transport, Wheel Extrapolations | Leave a comment

If I We’re a Landscaper

In overhauling and expanding the code’s formal PDF, I have come to appreciate just how much space is devoted to abstract reasoning behind the applications, and how far GDCode may seem to be removed from reality.

But in reviewing the math for wave-formed landscaping recently, I found it easier to make the connection with the volume of DIRT required to realize a plan. Before showing how useful the formulas are, here’s a brief description of how they were derived:

For half waves spun about their crests or troughs to shape mounds or round berms and embankments I used the thin shell integration method on the wave equation Y = M cos X, with Y being the height, M the maximum slope, X the radius and dx the thickness of the cylinder. I treated a quarter wave section at a time and spun from both directions to account for concave rounding situations.

Landscaping Wave Volumes

After integrating the convex crest quarter wave section, I divided this generalized volume by that of the cylinder bounding it to obtain a proportionality constant. For the concave trough volume, the convex crest volume is subtracted from the same cylindrical volume and divided by same to obtain its proportionality constant.

Wave Volume Integrations

The same procedure was used for the concave crest and the convex trough, but as these are separated from the pivot, the integrating limits are shifted from π/2 to π and proportioned to the volume of the (thick) cylindrical shell bounding them. I then I found I could multiply the proportionality constants by the volume of a wave-bounding cylindrical shell in a specified situation to obtain a real waveform’s volume.

I am not absolutely certain that this is a valid approach for volumes of waves spun about axes, but it seems reasonable and the relative size of the constants derived are consistent with what one would expect. For the derived constants and formulas, check out the new PDFs when they are published in a few weeks on this website.

Wave Area

What I am more certain of is taking the area of the wave cross-section and multiplying it by the length of an architectural embankment to determine its volume. Still, it seems strange that the constant does not depend on slope but the more one studies a range of slopes the more this makes sense.

Volume is important for two simple related reasons. Obviously, when one lays out a landscaping plan, quantity of dirt required is of great importance. The second value comes at the end of the embanking procedure which commences with determining and marking the wave’s height and width and their relationship keyed to the maximum slope chosen from a small set of options.

Waveform Embanking Basics

The next task is to stake out a string to signify the maximum slope which is half way between both the height and width. The next thing is to drive pointed rods every few feet with flat pieces angled to the maximum slope secured to the rod at the height of the string and extending upward.

Waveform StakingNext the dirt is piled in such a way that the crest and trough are horizontal and the steepening curvature of slope from the crest jives with the stakes’ board slope along the string. Upon satisfying these basic conditions, any remaining dirt is placed at the most glaring deficits eyeballed. If dirt is consumed before satisfying these conditions, material shift from excess to deficits is in order.

In my mind, this procedure was the most one could do without getting into high tech instruments. Then I explained what I was doing to my father (whose livelihood entailed working with road construction engineers) and he quickly pointed out the identical mirror image nature of the top and bottom wave portions.


Straight Slope embankments with mirror waves

Properly enlightened, I saw that the dirt volume in its entirety could then be piled up in a straight slope from top to the outward boundary. Dirt could then be sluffed away from the midline and placed directly above the string with full knowledge that the two volumes are equal as should be. Much better way. To perfect the slopes, mirror guides can be cut from a sheet of plywood.

This would work well for a symmetric wave and even though such is unnecessary or even impractical in many situations, it still poses the simplest, most elegant default waveform. All that remains is to plant the ground cover decided upon and wait for the waveform to unite the abode with the earth.

Posted in Code Application, Code History, Derivations, Ground Rules | Leave a comment