Supply your colonists with food, water and a breathable atmosphere. Give them jobs such as doctor, miner, or farmer. Colonists have feelings. They get upset when their friends are accidentally jetissioned out of air locks. If you're not careful, they'll opening rebel and attempt to destroy you.
Keep them happy, or supress dissent by force. Not only did this eliminate the pesky arrows, it reduced the total number of rooms in the map by half! Once I had mastered this technique, the next step was to use symmetry to break the remaining eight dimensions into sixteen smaller four-dimensional mazes which could then be arranged in a simple four-by-four grid.
This is possible because an 8-cube can be understood as a 4-cube tesseract in which each corner is itself a tesseract. It is relatively easy to draw the map of a tesseract, since it has only 16 rooms and 32 passages. As I burrowed into this problem, I developed my own private language , with terms like yin cells and yang cells. The overall structure of the map was now clear to me. By holding the center and yin corner cells constant and allowing only the remaining four yang cells to vary, I would create a tesseract of 16 rooms.
These rooms would be arranged in a four-by-four grid and linked by colored pipes that created a one-way flow from all yang cells solid to all yang cells empty. I called this mini-map a microcosm. Once I had one microcosm defined, I could create another by flipping a single yin cell.
Flipping through all 16 combinations of yin cells created a total of 16 microcosms. I would then arrange these 16 microcosms in the same sort of four-by-four grid and connect them with "macropipes".
Each macropipe would represent or contain the 16 pipes leading from a room in one microcosm to the corresponding room in another microcosm. In practice I had to divide each macropipe into four pipes, but this still reduced the total number of pipes in the map by a factor of four. To finish, all that was needed was a series of "center-pipes". Each center-pipe would contain pipes representing the change that takes place when a player clicks the center cell of a pattern.
Again, each center-pipe contained 16 smaller pipes and because of way the microcosms were defined, only one center-pipe was needed to connect each pair of center-related microcosms. After much experimentation, I discovered that I could further reduce the visual clutter by tilting each microcosm 45 degrees.
That was the theory, but in practice it was very hard to build each microcosm and wire them all together so that everything worked. One stumbling block was the orientation problem. At first I thought I could draw each room so that the northwest cell went out the northwest pipe, the north cell went out the north pipe, etc. But I soon discovered that this is impossible. To see why, just try deforming a map of the earth so that it is stretched across the six faces of a cube.
If you look at any of the six faces, it seems simple to draw in the points of a compass. But if you follow the north arrow off one face and cross over to an adjoining face a strange thing will happen. Instead of moving north you are now moving east. Or west. Or south! No matter how you rearrange your compasses, there is no way to get them all to connect together in a consistent way.
Try it yourself. For the starmap, this added a subtle complication. In one room, the northwest cell might feed into the northwest pipe.
But in a nearby room, the northwest cell might feed into the southeast pipe. I could correct for this by adding more pipes winding around each room, but that would have greatly increased the complexity and size of the map.
Instead I just defined a compass orientation for each room. It turned out that there were 16 different orientations in the starmaze, and now I had to create and keep track of a meta-map which described which rooms used which orientations. What made it worse was that nothing was fixed. I could connect the 16 rooms of a microcosm in a myriad of different ways, and each way would require a different meta-map of orientations.
Every time I fixed one problem, another would spring up somewhere else. So half of the houses, the houses with an even number of round or square yin cells, only allow movement from private up to public via the secret winding staircases.
I call these female houses. The other half, those with an odd number of round or square yin cells, only allow downward movement via fireman's poles. I call these male houses. Each male house is surrounded by four female houses and vice versa.
The female houses open outward and the male houses turn inward. Thrones The central organizing principle of the 3D starmaze is the five-level house in which public chambers trickle steadily downward and private chambers trickle steadily up, all based on movements through yang cells. But in a way this is unfair because yin cells trickle too. If you come to a pattern with four open yin corner cells, and resolve to move for a time only by choosing yin cells, the choices before you will narrow steadily down in exactly the same way that choices narrow within a house.
But since these are yin cells, each movement will carry you to a different house, two horizontal crossings and two vertical crossings, leading you inexorably, regardless of order, to the opposite house from the one you started in. This pattern of choices forms an invisible, virtual house that stretches across five real houses.
This virtual trickle pattern is often a useful way to navigate the maze and understand its changing patterns. So even though yang cell shifts are the established way of trickling in the 3D starmaze, I needed a way of marking these virtual yin cell trickles as well. Hence, the throne. A throne represents the top or "seat" of a virtual yin trickle pattern.
It occurs whenever a pattern has four open yin cells. Since yin cells are not affected by movements through the center cell, a throne belongs to both the public and private chambers of whatever room it occurs in. There are 16 throne rooms scattered throughout the maze in a particular way.
Because yang cell shifts preserve parity add or subtract 0 or 2 to the number of open yin cells , a house which starts with an even number of yin cells will stay that way in every room. Thus all even-numbered yin cell patterns occur in female houses and all odd-numbered yin cell patterns occur in male houses.
And because a throne room with four open yin cells is an even-numbered pattern, the 16 thrones occur only in female houses; each female house contains two throne rooms. Only queens, not kings, sit on starmaze thrones. The symmetry of the binary trickle causes the two throne rooms in every female house to occur in precisely opposite positions. This means that if one throne occurs in room n, the other will occur in room n. In order to make these thrones easier to remember and distinguish, I have assigned each throne a name which refers to the substance the throne is made of or in some cases the decorations with which it is crafted.
The five virtual levels in these virtual houses are given names instead of numbers. The room containing the throne itself is called the "seat". Crossings taken in any order lead to one of four rooms, each called a dais, then to one of six rooms, each called a step, then to one of four more rooms, each called a foundation, and finally to the terminus of the throne, always located in the opposite house from the seat.
All of these rooms are said to bear "allegiance" to their throne. If I ever get around to interior decoration, I plan to mark this by placing appropriate ornaments of allegiance in every room.
Discoveries The starmaze in general, and my attempt to build a realistic 3D starmaze in particular, has from the beginning been a ponarv , a project of no apparent redeeming value. I did not begin this project with the intention of discovering anything useful, but, as always happens, I have already learned a thing or two along the way, and by seeking nothing may accomplish much. The first insight is that empty buildings are mostly made of passages.
I used to think of the starmaze as primarily a collection of rooms, each room having significant weight and volume. But as I toil away, laying virtual bricks one at a time, I find that my rooms are dwarfed by the vast network of stairs and bridges and hallways. This might change once the rooms are filled with furnishings and bric-a-brac intricately arranged.
But empty rooms are easily designed, easily made, and easily lost amidst all the little pieces needed to knit rooms together. Now as I hold the starmaze in my mind, I feel the weight of all those connecting pieces. To really see and understand any multi-room building, you have to see and understand how it is put together. Obvious in hindsight, but now I know it in my bones. Starmaze passages consume more "psychological" space but, as it turns out, not more actual surface area.
It is tedious to calculate the exact amount of square feet consumed by every twisting passage and staircase, but when I did a partial survey I was astonished to discover that the total surface areas of rooms and passages are roughly equal.
There are rooms in the bastions that look like narrow shelves when seen from above, but which consume more square feet than the house I am currently living in. So a second insight is that psychological space and physical space are not at all the same. I have also discovered that three-dimensional space is not as roomy as I thought.
The footprint of the starmaze complex consumes about a million square feet. It reaches more than twenty stories into the air and burrows deep underground. Given all that, I assumed I would have no trouble weaving my passages without unwanted intersections.
I soon learned otherwise. It was often surprisingly hard to find a way to connect the rooms in the way required without collisions.
I had to survey the scene from every angle, squeeze into tight corners, and come up with ingenious out-of-the-box solutions just to make one connection. I would then realize that three more connections had to be routed through the very space I had just filled so tightly. In some cases I was eventually forced to loosen my restrictions and allow passages to merge and split before arriving at their appointed monolith. As mentioned above, the most pleasant surprise has been the way that even basic shapes and enclosures convey a sense of personality.
Even without furnishings, each room in my Sketchup model has a distinctive "feel". We are deeply spatial creatures, and are hardwired not just to comprehend space with our heads but to feel it with our hearts.
This "Feng Shui" is a real phenomenon which I could not have encountered through a purely mathematical model. It may prove useful as a way of adding further depth and meaning to the patterns of the maze. In addition to these basic discoveries about the nature of space, I continue to have many small epiphanies about particular ways in which the starmaze functions. The more vivid visualizations afforded by the realistic 3D layout allow me work out many problems entirely in my head - which is exactly what I hoped would happen.
My goal now is to turn the starmaze into a "memory palace" so vivid that I will be able to calculate the shortest path between any two patterns by simply seeing the answer. The construction of memory palaces is a lost art; I hope the discoveries I am making about space and feelings and verisimilitude will help me find a way.
Stone Soup In the classic Grimm Brothers tale, returning soldiers convince selfish villagers to share their food by telling them they are making "stone soup". They place a stone in a pot of water and start it boiling. One by one they get each suspicious villager to add an apparently inconsequential ingredient until a flavorful soup comes together that is more than the sum of its parts.
I often think of the starmaze as a kind of stone soup. The "stone" is the basic mathematical structure which, glorious though it is, is really nothing more than a big square. To this sterile beginning I add a label to clarify a particular insight, and then another, inevitably using words as metaphors to convey each new concept. Though I try to use them carefully, each new word leaves behind a residue of excess meaning, rubbing off flavors and evoking associations the way all words do.
The corners of the stone become "houses" and acquire shapes tower, bastion, courtyard, deep. Each shape moves in four directions and the directions acquire terrains forest, desert, ocean, mountain. Their properties acquire labels, yin and yang, sun and moon, seasons, elements, forms.
Each house gets its own name: darkness, sand, rumor, rain. Thrones appear of carnelian and iron, emerald and onyx. The more I look, the more I see. The more I see, the more new words I need. Monolith, oculus, trickle, microcosm, macropipe, dais, grotto, keeper, key, channel, crossroad, subway, temple, terminus. It may turn out that the greatest power of the 3D representation of the starmaze is the net of meaning it creates through this gradual accumulation of terminology.
Indeed, my next big project will be to finally assign names to each pattern. According to the official developers page for the accelerometer , " Nokia expects to introduce the 3D accelerometer technology to other devices in the future ", so they're clearly not planning the to be a one-off.
Perhaps if the accelerometer is cheap and compact enough, and the is certainly both of those things, it could eventually be included as standard feature, just like vibrating alert technology. The memory card that comes with the includes a S60 3rd Edition game called Groove Labyrinth which uses the accelerometer as a tilt sensor. The sensor allows the player to control the game by simply tilting the phone in the direction of travel, with the angle of tilt controlling the speed of travel like one of those plastic maze toys where you have to manoeuvre a metal ball through it.
It's somewhat similar to the old s classic Marble Madness, and the aim is to tilt the environment so that the ball can travel through a course while avoiding the edges and various other traps. Each level can be cleared by picking up every jewel and reaching the exit before the time runs out. Along the way the player encounters bonuses extra time, extra lives, shields, teleports and dangers collapsing floors and mines. The view of the game is top down, with the 3D landscape visible directly beneath the player.
Using the game is odd at first, it's strange that real world actions are replicated in the game, but perhaps the first ever mouse-based games on home computers felt the same way. Once you get used to simply moving the phone and not pressing any buttons it all feels very natural however.
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