(please enlarge the window to at least 800x830!)
"); ##maybe have that CRF image and a KB myDiv1a is Div("div1a",20,20,360,360,"When a person or an animal looks at something, a specific bunch of neurons in their brain will start flashing. There are a lot of patterns connecting what neurons fire in reponse to what sights, and these patterns can be very complex. Your head is filled with intricate mathematics - whether you feel that way or not.
Today we’re going to try to understand some of the patterns in your head that allow you to perceive things. We’ll do this by examining some of the neurons, we’ll look at some pictures that the neurons will respond to, and we’ll have ‘maps’ of the neurons you get in the visual cortex. More specifically, we’re going to think about a theory developed by Shigeru Tanaka regarding neuron responses in the ‘visual cortex’.
Let’s say that that picture down there is a neuron inside your head. It’s connected to a certain ‘sight’. Try and find out what that ‘sight’ is.
"); myDiv1b is Div("div1b",20,20,360,360,"When a person or an animal looks at something, a specific bunch of neurons in their brain will start flashing. There are a lot of patterns connecting what neurons fire in reponse to what sights, and these patterns can be very complex. Your head is filled with intricate mathematics - whether you feel that way or not.
Today we’re going to try to understand some of the patterns in your head that allow you to perceive things. We’re going to examine some neurons, we’ll look at some pictures that the neurons will respond to, and we’ll have ‘maps’ of neurons in the visual cortex. Specifically, we’re thinking about a theory developed by Shigeru Tanaka regarding neuron responses in the ‘visual cortex’.
Let’s say that that picture down there is a neuron inside your head. It’s connected to a certain ‘sight’. Try and find out what that ‘sight’ is.
Great! So it turns out that this neuron fires when there is movement inside of the rectangle on the right. The things we’re going to look at will work like that, except with more neurons, and with different sights.
"); myDiv2 is Div("div2",20,20,360,360,"We’re going to look at how neurons respond to straight lines, specifically their ‘orientation’, and later their ‘direction of travel’. Some of the neurons in your brain will only have a chance of lighting up when you’re looking at a line, like the ones below. Before moving on, try and see if you can get them both to light up at the same time.
In general, neurons that are close to one another will respond to similar things, like these two which respond to orientations that are almost the same. That’s part of the thing that generates the mathematical patterns that you’re going to experience.
Also, we’re certainly not just talking about your brain responding to boring black lines on a computer screen! The neurons we’re talking about here are going to be involved in processing the sight of ANY line that you might see in your day to day life, like a spinning helicopter blade, or a chopstick you’re about to put into your mouth, or how about this: a line of black feathers going across the wings of a bird...
"); myDiv3 is Div("div3",20,20,360,360,"So there’s a bird! Your brain perceives that strip of feathers as a line, so the neurons that this presentation is about will fire when you look at it.
We’re now looking at things a different way than in the previous slide. We’re pretending that the square down there is full of neurons, ok? Anywhere you click in it will contain a neuron. The orientation of that albatross is going to be causing a neuron to flicker - she’s going to rotate to a position where she’s activating the neuron you’ve chosen.
See if you can get her to point East-Northeast. When you’ve done that, try to get her to point straight down - you’ll find that you can’t go far enough. You’ll see that this isn’t just because of the way I’ve built the program, it’s actually a limitation your brain has. If our albatross were pointing downwards, *these* neurons would activate exactly the same as if she were pointing in the exact opposite direction. They just can’t tell ‘which way up’ a line is supposed to be when they see one, so in order for you to sense the difference, your brain would probably have to get a bunch of other neurons involved. If you want to fully understand this, you might find it helpful to go back to the previous page with this in mind: there is actually more than one line-orientation that was able to make those two neurons light up. And feel free to go back and forth as much as you like by the way!
"); myDiv4 is Div("div4",20,20,360,360,"Now in actual fact, the neurons are laid out in a more complicated way than on that previous ‘field’. Again, pretend the square below is filled with neurons. When you fiddle with this, you’ll find that the layout ‘loops around’ a bit.
Remember, by the way, that neurons are really small! Inside your head, the field of cells you’re clicking around here is about a 1mm wide area.
Incidentally, those highlighted points are called ‘singularities’; they’re places where the neuron response is very weird - if there’s any response at all. If you experiment with this field, you’ll realize that any response there would be a bit out-of-place. If you want a bit of a challenge, see if you can drag from one singularity to another while making the albatross change direction as little as possible. Note that this means that a certain orientation can have a whole bunch of different neurons that respond to it.
"); myDiv5 is Div("div5",20,20,360,360,"Neurons are seldom straightforward things, and they often do more than one job. The cell fields we’ve been talking about so far will also light up differently when there’s a line *travelling* in a certain direction. The field below is the same as before, but now the albatross is going to be travelling, as well as turning, with the orientation and direction that’s bound to the neuron you select.
Try to get our albatross to fly in every different direction. Or perhaps try to make the albatross fly directly left, then right. You’ll find it’s a bit complicated! And there’s a weird dependency between orientation and direction for a given neuron.
Really we’d prefer to be able to select any orientation and direction and see how the neurons respond. So we’re going to bring in a mathematical tool that’ll let us do this.
"); myDiv6 is Div("div6",20,20,360,360,"Ok now the square down there is still the neuron field, but this time, instead of directly choosing a neuron, you’re going to use that square on the right to control the albatross. The neurons are going to be lighting up in response to the albatross’s current orientation and direction; those wiggly lines are chains of lit-up neurons. The white neurons would be responding to the orientation, and yellow ones to the direction (if they overlap then that means the neurons are firing like crazy!).
Try making the albatross do two loops in a row. You’ll find you can’t do it - that’s a problem, you ought to be able to! What we need to do is make it so you can cross over the edge of the square, taking you to the other side. In other words, we need to glue the sides of the square together - and it turns out that if we do this properly, we get a weird shape which you’ll see in the next slide.
So to recap: you’re looking at a square that allows you to choose an ‘orientation’ and a ‘direction’ (right); you also have a bird flying with the direction and orientation you’ve chosen; and you have a snapshot of a small area of your brain with lit-up neurons (below); and replacing these words, you’re going to see a connected-up version of your square.
"); myDiv8 is Div("div8",20,20,360,360,"Klein bottles are really interesting objects, for mathematicians. Lots of mathematicians want to know what can happen with shapes that are completely ‘smooth’. The Klein bottle is special because its inside has direct connections to its outside, and all those connections are smooth. It’s also a shape that can only be seen properly in ‘four dimensions’!
For more than a century, the Klein bottle has studied and delighted over by mathematicians. And in all that time, it never has had a single use outside of mathematics - that was until Shigeru Tanaka came up with this theory about neurons! I personally find it very lovely that brains work in these intricate ways that studying them requires knowledge of such esoteric objects.
"); myDiv9 is Div("div9",20,20,360,360,"There’s an important pattern that connects the bottle and the singularities; you might be able to work it out. Try doing different ‘loops’ on the rectangle / bottle while looking at what happens on the neuron field. Can you work out how to do a loop that will make those lines go all the way around around the singularities?
A lot of scientists are interested in how, why, and where the singularities arise in these neuron fields - using the Klein bottle in this way can help answer some of their questions.
"); myDiv10 is Div("div10",20,20,360,360,"It’s worth saying that in reality, there are waaay more than two singularities. These fields have many thousands of neurons, and with loads of singularities among them, about four per millimeter. You’ll have noticed there are two kinds of singularity, blue and orange - can you see what the difference is between them?
By the way, the place you move over that causes the albatross to swivel is called a ‘line singularity’ - can you see a relationship between the line singularities and the ‘point’ singularities?
That’s the end of the presentation now - hope you’ve enjoyed it!
"); ##the first page rectline1 = Line( 500,500,700,500); rectline2 = Line( 500,500,500,700); rectline3 = Line( 700,500,700,700); rectline4 = Line( 500,700,700,700); mouseposition is mouseX + mouseY * 800; timesinceneuronwasinactive = 0; neuronvictory = 160; cellOn = Image("1on",0,400,400,400,"http://s17.postimg.org/ynp1mocsv/onx.png"); cellOff = Image("1off",0,400,400,400,"http://s17.postimg.org/pc2zpq09b/offx.jpg"); proc mousemovinginrect : mouseposition { if( mouseX > 500 && mouseY > 500 && mouseX < 700 && mouseY < 700 ) { ##turn over an hourglass that is counted down by step timesincemousemovement = 12; } } proc mousemovementchecker : step { ##only do this if we're on the right slide if( slidenumber != 1 ) return; ##This is always being counted down timesincemousemovement--; ##Is the neuron still lit up from the last movement? if( timesincemousemovement > 0 ) { timesinceneuronwasinactive++; ##have we won yet? (don't forget to tweak both appearances of this number) If so, div changes. If not, we still want to see a different picture if( timesinceneuronwasinactive > neuronvictory ) picture is [myDiv1b, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, rectline1, rectline2, rectline3, rectline4,cellOn]; ##plus extra picture else ##neuron's lit up but we've not won picture is [myDiv1a, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, rectline1, rectline2, rectline3, rectline4,cellOn]; ##plus extra picture } ##haven't been stimulated for a while, we get the boring picture else { ##neuron's inactive if( timesinceneuronwasinactive < neuronvictory ) { timesinceneuronwasinactive = 0; picture is [myDiv1a, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, rectline1, rectline2, rectline3, rectline4,cellOff]; } else { ##neuron's still inactive, but we've already won and so don't care about that variable picture is [myDiv1b, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, rectline1, rectline2, rectline3, rectline4,cellOff]; } } } ##second page mousedist is sqrt( (600 - mouseX)*(600 - mouseX) + (600 - mouseY)*(600 - mouseY)); cellOffOff = Image("2ff",0,400,400,400,"http://s17.postimg.org/p0ljcyjtb/2cells0.png"); cellOnOff = Image("2nf",0,400,400,400,"http://s17.postimg.org/rvymjtntb/2cells1.png"); cellOffOn = Image("2fn",0,400,400,400,"http://s17.postimg.org/9wzd8uxfz/2cells2.png"); cellOnOn = Image("2nn",0,400,400,400,"http://s17.postimg.org/6ouvvtb67/2cells3.png"); plainline1 is Line(600,600, (600+(600-mouseY) / mousedist * 100), (600-(600-mouseX) / mousedist * 100)); plainline2 is Line(600,600, (600-(600-mouseY) / mousedist * 100), (600+(600-mouseX) / mousedist * 100)); plainangle is atan((mouseX - 600)/(mouseY - 600)); ##might need atan2 thing filteredplainangle is ( plainangle < 0 ) ? 180 + plainangle : plainangle; proc secondpagemonitor : filteredplainangle { if( slidenumber != 2 ) return; picture is ( 141.4 <= filteredplainangle && filteredplainangle < 148 ) ? [myDiv2, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, cellOnOff,plainline1,plainline2] : ( 134 <= filteredplainangle && filteredplainangle < 140 ) ? [myDiv2, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, cellOffOn,plainline1,plainline2] : ( 140 <= filteredplainangle && filteredplainangle < 141.4 ) ? [myDiv2, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3, cellOnOn,plainline1,plainline2] : [myDiv2, nextButton, prevButton, prevarrow1, prevarrow2, prevarrow3, nextarrow1,nextarrow2,nextarrow3,cellOffOff,plainline1,plainline2]; } ##third page basicneuronsrect = Rectangle(20, 420, 360,360, "Black","Black"); highlightedneuronX = 0; highlightedneuronY = 0; basicneuronspoint is Circle(highlightedneuronX + 20,highlightedneuronY + 420, 3 + sin( step * 2 ) * 1, "Yellow" ); proc neuronmover : mousePressed { ##if they've just let go, we fix everything if( !mousePressed ) { ##player has just let go of the mouse highlightedneuronX = highlightedneuronX; highlightedneuronY = highlightedneuronY; return; } ##if they've just pressed down, we're only interested if it's in the rectangle if( mouseX < 20 || mouseY < 420 || mouseX > 20 + 360 || mouseY > 420 + 360 ) return; ##player has just clicked in rectangle. Make indicator follow mouse highlightedneuronX is (0<=mouseX - 20 && mouseX - 20 < 360 )? mouseX - 20 : (mouseX -20 < 0) ? 0 : 360; highlightedneuronY is (0 <= mouseY- 420 && mouseY- 420 < 360 )? mouseY - 420 : (mouseY -420 < 0) ? 0 : 360; } ##here is where you'd change it so that the flip's in right place. ##PUT THIS IN SLIDECHANGER theta is ( highlightedneuronX + highlightedneuronY ) / 4; ##this one requires step. ##6th fakedomain = Rectangle(420,20,360,360, "DeepSkyBlue"); fakeindicatorX = 0; fakeindicatorY = 0; fakeindicator is Circle(fakeindicatorX+420,fakeindicatorY+20,indicatorR, "White", "White"); proc fakeindicatormover : mousePressed { ##if they've just let go, we fix everything if( !mousePressed ) { ##player has just let go of the mouse fakeindicatorX = fakeindicatorX; fakeindicatorY = fakeindicatorY; return; } ##if they've just pressed down, we're only interested if it's in the rectangle if( mouseX < 420 || mouseY < 20 || mouseX > 420 + 360 || mouseY > 20 + 360 ) return; ##player has just clicked in rectangle. Make indicator follow mouse fakeindicatorX is (0<=mouseX - 420 && mouseX - 420 < 360 )? mouseX - 420 : (mouseX -420 < 0) ? 0 : 360; fakeindicatorY is (0 <= mouseY- 20 && mouseY- 20 < 360 )? mouseY - 20 : (mouseY -20 < 0) ? 0 : 360; } ##7th page Kleinanimation = Image("Kleingif",400 + 123, 100, 154, 192, "http://s23.postimg.org/ubikf9w8r/imageedit_1_8596514619.gif"); Beer = Image("Drink",427,400,345,399,"http://s24.postimg.org/4pkufx9d1/Beer.jpg"); Kleinanimation2 = Image("KG2",123, 504, 154,192,"http://s28.postimg.org/an5phyril/Mobius_Klein.gif"); ##10th ##fs “final singularity” fs1X = 20 + rand() % 360; fs1Y = 420 + rand() % 360; fs2X = 20 + rand() % 360; fs2Y = 420 + rand() % 360; fs3X = 20 + rand() % 360; fs3Y = 420 + rand() % 360; fs4X = 20 + rand() % 360; fs4Y = 420 + rand() % 360; fs5X = 20 + rand() % 360; fs5Y = 420 + rand() % 360; fs1 = Image("fsI",fs1X+4,fs1Y-2, 14,14, "http://s29.postimg.org/vl947rfqb/Whirlpool_1.png"); fs2 = Image("fsII",fs2X+4,fs2Y-2, 14,14, "http://s17.postimg.org/79xhd3ikb/Whirlpool_2.png"); fs3 = Image("fsIII",fs3X+4,fs3Y-2, 14,14, "http://s17.postimg.org/79xhd3ikb/Whirlpool_2.png"); fs4 = Image("fsIV",fs4X+4,fs4Y-2, 14,14, "http://s17.postimg.org/79xhd3ikb/Whirlpool_2.png"); fs5 = Image("fsV",fs5X+4,fs5Y-2, 14,14, "http://s29.postimg.org/vl947rfqb/Whirlpool_1.png"); ##general things func angleattribution { para pointX, pointY,singularityX,singularityY; auto relativeY, relativeX,orientationangle; relativeX = pointX - singularityX; relativeY = pointY - singularityY; if( relativeX == 0 && relativeY == 0 ) return 0; if(relativeY < 0 && relativeX >= 0) orientationangle = 0 - 0.5 * atan(relativeX/relativeY); if(relativeY >= 0 && relativeX > 0) orientationangle = 45 + 0.5 * atan(relativeY/relativeX); if(relativeY > 0 && relativeX <= 0) orientationangle = 90 - 0.5 * atan(relativeX/relativeY); if(relativeY <= 0 && relativeX < 0) orientationangle = 135 + 0.5 * atan(relativeY/relativeX); return orientationangle; } singularity1X = 90 + 20; singularity1Y = 90 + 420; singularity2X = 270 + 20; singularity2Y = 270 + 420; singularity1pic is Image("whirlpool",singularity1X+4,singularity1Y-2,14,14,"http://s29.postimg.org/vl947rfqb/Whirlpool_1.png"); singularity2pic is Image("whirlpool2",singularity2X+4,singularity2Y-2,14,14,"http://s17.postimg.org/79xhd3ikb/Whirlpool_2.png"); domainW = 360; domainH = 360; domainX = 420; domainY = 20; ##this is the rectangle with a thing that wraps domainRect = Rectangle(420,20,360,360,"DeepSkyBlue"); ##gridlineH1, gridlineH2, gridlineH3, gridlineH4, gridlineH5, gridlineH6, gridlineH7, gridlineH8, gridlineH9, gridlineH10, gridlineH11, gridlineH12, gridlineH13, gridlineH14, gridlineH15, gridlineV1, gridlineV2, gridlineV3, gridlineV4, gridlineV5, gridlineV6, gridlineV7, gridlineV8, gridlineV9, gridlineV10, gridlineV11,gridlineV12, gridlineV13,gridlineV14, gridlineV15, ##we have a thing that you pick up and drag indicatorX = domainY + domainH/2; indicatorY = domainX + domainW/2; flythroughcountX = 0; flythroughcountY = 0; reflection = 0; ##has the player just let go of or presed down the mouse? proc indicatormover : mousePressed { ##if they've just let go, we fix everything if( !mousePressed ) { ##player has just let go of the mouse indicatorX = indicatorX; indicatorY = indicatorY; flythroughcountX = flythroughcountX; flythroughcountY = flythroughcountY; reflection = reflection; return; } ##if they've just pressed down, we're only interested if it's in the rectangle if( mouseX < domainX || mouseY < domainY || mouseX > domainX + domainW || mouseY > domainY + domainH ) return; ##player has just clicked in rectangle. Make indicator follow mouse indicatorY is mouseY - flythroughcountY * domainH; indicatorX is mouseX - flythroughcountX * domainW + reflection * ( domainW - (mouseX -domainX - flythroughcountX * domainW) - (mouseX-domainX - flythroughcountX * domainW) ); ##this line combats the normal value flythroughcountX is (mouseX - domainX - ((mouseX-domainX + 10*domainW) % domainW)) / domainW; flythroughcountY is (mouseY - domainY - ((mouseY-domainY + 10*domainW) % domainW)) / domainW; reflection is (flythroughcountY+20) % 2; } indicatorR = 2; indicator is Circle(indicatorX,indicatorY,indicatorR, "White", "White"); ##h is height of "cone", r is radius of bend, f is height of funnel. f = 30; h = 240; r = 60; bottlewidth = r; bottlehight = r / 3; KBPosition = 0; bottleOffsetX is ( KBPosition == 0 ) ? 169 : 569; bottleOffsetY is (KBPosition == 2 ) ? 459 : 59; spineX = 0; spineY = 0; ellipseangle = 0; ##this is the spine of the bottle. 0 is at the boundary between the funnel and cone We divide the whole into the four parts. spineY is ##funnel ( 0 <= theta && theta < 45 ) ? -f * sin(4 * theta) : ##cone ( 45 <= theta && theta < 90 ) ? h * (theta - 45) / 45 : ##bend ( 90 <= theta && theta < 135 ) ? h + r * sin( 4 * (theta - 90)) : ##pipe (135 <= theta && theta < 180 ) ? h * (180 - theta) / 45 : 0; ##failsafe spineX is ##funnel ( 0 <= theta && theta < 45 ) ? 0 : ##cone ( 45 <= theta && theta < 90 ) ? 0 : ##bend ( 90 <= theta && theta < 135 ) ? r - r * cos( 4 * (theta - 90)) : ##pipe (135 <= theta && theta < 158 ) ? 2 * r - (theta - 135) * (theta - 135) / 23 / 23 * r : (158 <= theta && theta < 180 ) ? (180-theta) * (180-theta) / 22 / 22 * r: 0; ##failsafe ##This is the dimensions of the elliptic cross section. We take the normal dimensions to be width = r, hight = r/3. bottlewidth is ##funnel - hopefully smooth ( 0 <= theta && theta < 45 ) ? 2 * r - r * cos( 4 * theta ) : ##cone - would be nice to make this smoother, ideally using the pipe's curve. ( 45 <= theta && theta < 90 ) ? r * ((90-theta) / 23 + 1) : ##other r; bottlehight is ##funnel - hopefully smooth ( 0 <= theta && theta < 45 ) ? r / 3 * (theta / 23 + 1) : ##cone ( 45 <= theta && theta < 90 ) ? r / 3 * ((90-theta) / 23 + 1) : ##bend ( 90 <= theta && theta < 135 ) ? r * (225-theta * 2) / 135 : ##pipe (135 <= theta && theta < 180 ) ? - r / 3 : ##other r / 3; ##there's also an angling of the ellipse. ellipseangle is ##bend ( 90 <= theta && theta < 135 ) ? (theta-90) * 4 : ##pipe - we want it to be the angle of the tangent to the line... could take the next point and aim at that (135 <= theta && theta < 158 ) ? 180 + atan((theta-135)/23) : ##this was not rigorous (158 <= theta && theta < 180 ) ? 180 + atan((180-theta)/22) : ##funnel, cone 0; ##the location of the points, with the correct point on the spine taken as the origin. bottlepointX is bottlewidth / 2 * cos(phi) * cos( ellipseangle) - bottlehight / 2 * sin(phi) * sin(-ellipseangle); bottlepointY is bottlewidth / 2 * cos(phi) * sin(-ellipseangle) + bottlehight / 2 * sin( phi) * cos( ellipseangle); finalpointX is bottleOffsetX + spineX + bottlepointX; finalpointY is bottleOffsetY + spineY + bottlepointY; Kleinimage is Image("Klein",bottleOffsetX-89,bottleOffsetY-51,241,383,"http://s30.postimg.org/5t2h58xdd/KBfinal.png"); proc colorchanger : phi { ##maybe you’re in the doubly covered part? if( ( theta > 154 && finalpointY - bottleOffsetY - 153 < (finalpointX - bottleOffsetX - 52) * -4 ) || (theta < 17 && finalpointY - bottleOffsetY + 13 > -1 * pow( (finalpointX - bottleOffsetX)/13,2) ) ) { pointimage = Image("pointblue", finalpointX - 2, finalpointY - 2, 6,6,"http://s17.postimg.org/z2mebuldn/bluepoint.png"); return; } ##the funnel is a special case of “front and back” if( theta < 45) { ##there’s kind of an ellipse across the grid? if( theta < 27 || !(180 < phi && phi < 360) || theta < 45 - 19 * sqrt( 1 - pow( ((270-phi)/90),2) ) ) pointimage = Image("pointwhite", finalpointX - 2, finalpointY - 2, 6,6,"http://s24.postimg.org/cwgiikyoh/point.png"); else pointimage = Image("pointblue", finalpointX - 2, finalpointY - 2, 6,6,"http://s17.postimg.org/z2mebuldn/bluepoint.png"); return; } ##we define the “front”, ignoring the self intersection because what can you do? if( phi > 180 ) pointimage = Image("pointblue", finalpointX - 2, finalpointY - 2, 6,6, "http://s17.postimg.org/z2mebuldn/bluepoint.png"); ##this back else pointimage = Image("pointwhite", finalpointX - 2, finalpointY - 2, 6,6,"http://s24.postimg.org/cwgiikyoh/point.png"); } crfX = 20; crfY = 420; crfW = 360; crfH = 360; step = 0; crfRect is Rectangle(crfX,crfY,crfW,crfH, "Black", "Black" ); intendedtheta is theta; intendedphi is phi; ##this treats top left corner of triangle as origin. func getXplus360y { para t; ##how many pixels are there in a triangle? 12 * layer * 22. Possible points? 22 * 12 ##we do it “array style” so this function only needs calling once! if( 0 <= t && t < 22 * 4 ) return t + 0; if( 22 * 4 <= t && t < 22 * 8 ) return 22 * 8 -t + 360 * (t - 22 * 4); if( 22 * 8 <= t && t < 22 * 12 ) return 0 + 360 * (22 * 4 - (t-22*8)); } func angleattribution { para pointX, pointY,singularityX,singularityY; auto relativeY, relativeX,orientationangle; relativeX = pointX - singularityX; relativeY = pointY - singularityY; if( relativeX == 0 && relativeY == 0 ) return 0; ##we’d like if(relativeY < 0 && relativeX >= 0) orientationangle = 90 - 0.5 * atan(relativeX/relativeY); if(relativeY >= 0 && relativeX > 0) orientationangle = 135 + 0.5 * atan(relativeY/relativeX); if(relativeY > 0 && relativeX <= 0) orientationangle = 0 - 0.5 * atan(relativeX/relativeY); if(relativeY <= 0 && relativeX < 0) orientationangle = 45 + 0.5 * atan(relativeY/relativeX); return (orientationangle + 90) % 180; } proc s2phipoint1mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( intendedphi > 270 || 90 > intendedphi ) { s2phipoint1X = 0; s2phipoint1Y = 0; return; } layer = 1; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2phipoint1phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2phipoint1t = ( (s2phipoint1t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2phipoint1t ); s2phipoint1X = -layer * (-22 + position % 360 ); s2phipoint1Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2phipoint1t = 0; ##could be -90 s2phipoint1phi is 90 + ( ( angleattribution(s2phipoint1X+singularity2X,s2phipoint1Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2phipoint1X+singularity2X,s2phipoint1Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2phipoint2mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( intendedphi > 270 || 90 > intendedphi ) { s2phipoint2X = 0; s2phipoint2Y = 0; return; } layer = 2; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2phipoint2phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2phipoint2t = ( (s2phipoint2t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2phipoint2t ); s2phipoint2X = -layer * (-22 + position % 360 ); s2phipoint2Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2phipoint2t = 0; ##could be -90 s2phipoint2phi is 90 + ( ( angleattribution(s2phipoint2X+singularity2X,s2phipoint2Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2phipoint2X+singularity2X,s2phipoint2Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2phipoint3mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( intendedphi > 270 || 90 > intendedphi ) { s2phipoint3X = 0; s2phipoint3Y = 0; return; } layer = 3; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2phipoint3phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2phipoint3t = ( (s2phipoint3t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2phipoint3t ); s2phipoint3X = -layer * (-22 + position % 360 ); s2phipoint3Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2phipoint3t = 0; ##could be -90 s2phipoint3phi is 90 + ( ( angleattribution(s2phipoint3X+singularity2X,s2phipoint3Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2phipoint3X+singularity2X,s2phipoint3Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2phipoint4mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( intendedphi > 270 || 90 > intendedphi ) { s2phipoint4X = 0; s2phipoint4Y = 0; return; } layer = 4; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2phipoint4phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2phipoint4t = ( (s2phipoint4t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2phipoint4t ); s2phipoint4X = -layer * (-22 + position % 360 ); s2phipoint4Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2phipoint4t = 0; ##could be -90 s2phipoint4phi is 90 + ( ( angleattribution(s2phipoint4X+singularity2X,s2phipoint4Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2phipoint4X+singularity2X,s2phipoint4Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s1phipoint1mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( 90 <= intendedphi && intendedphi <= 270 ) { s1phipoint1X = 0; s1phipoint1Y = 0; return; } layer = 1; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1phipoint1phi - intendedphi; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##change? ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1phipoint1t = ( (s1phipoint1t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1phipoint1t ); s1phipoint1X = layer * (-22 + position % 360 ); s1phipoint1Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1phipoint1t = 0; s1phipoint1phi is ( 270 + ( ( angleattribution(s1phipoint1X+singularity1X,s1phipoint1Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1phipoint1X+singularity1X,s1phipoint1Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180 ) % 360; proc s1phipoint2mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( 90 <= intendedphi && intendedphi <= 270 ) { s1phipoint2X = 0; s1phipoint2Y = 0; return; } layer = 2; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1phipoint2phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1phipoint2t = ( (s1phipoint2t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1phipoint2t ); s1phipoint2X = layer * (-22 + position % 360 ); s1phipoint2Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1phipoint2t = 0; s1phipoint2phi is ( 270 + ( ( angleattribution(s1phipoint2X+singularity1X,s1phipoint2Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1phipoint2X+singularity1X,s1phipoint2Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180 ) % 360; proc s1phipoint3mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( 90 <= intendedphi && intendedphi <= 270 ) { s1phipoint3X = 0; s1phipoint3Y = 0; return; } layer = 3; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1phipoint3phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1phipoint3t = ( (s1phipoint3t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1phipoint3t ); s1phipoint3X = layer * (-22 + position % 360 ); s1phipoint3Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1phipoint3t = 0; s1phipoint3phi is ( 270 + ( ( angleattribution(s1phipoint3X+singularity1X,s1phipoint3Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1phipoint3X+singularity1X,s1phipoint3Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180 ) % 360; proc s1phipoint4mover : step { auto layer, distance, clockwise, position; ##there are values these points can’t do if( 90 <= intendedphi && intendedphi <= 270 ) { s1phipoint4X = 0; s1phipoint4Y = 0; return; } layer = 4; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1phipoint4phi - intendedphi; ##s1 has -90 if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1phipoint4t = ( (s1phipoint4t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1phipoint4t ); s1phipoint4X = layer * (-22 + position % 360 ); s1phipoint4Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1phipoint4t = 0; s1phipoint4phi is ( 270 + ( ( angleattribution(s1phipoint4X+singularity1X,s1phipoint4Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1phipoint4X+singularity1X,s1phipoint4Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180 ) % 360; proc s2thetapoint1mover : step { auto layer, distance, clockwise, position; layer = 1; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2thetapoint1theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2thetapoint1t = ( (s2thetapoint1t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2thetapoint1t ); s2thetapoint1X = -layer * (-22 + position % 360 ); s2thetapoint1Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2thetapoint1t = 0; s2thetapoint1theta is ( ( angleattribution(s2thetapoint1X+singularity2X,s2thetapoint1Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2thetapoint1X+singularity2X,s2thetapoint1Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2thetapoint2mover : step { auto layer, distance, clockwise, position; layer = 2; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2thetapoint2theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2thetapoint2t = ( (s2thetapoint2t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2thetapoint2t ); s2thetapoint2X = -layer * (-22 + position % 360 ); s2thetapoint2Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2thetapoint2t = 0; s2thetapoint2theta is ( ( angleattribution(s2thetapoint2X+singularity2X,s2thetapoint2Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2thetapoint2X+singularity2X,s2thetapoint2Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2thetapoint3mover : step { auto layer, distance, clockwise, position; layer = 3; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2thetapoint3theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2thetapoint3t = ( (s2thetapoint3t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2thetapoint3t ); s2thetapoint3X = -layer * (-22 + position % 360 ); s2thetapoint3Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2thetapoint3t = 0; s2thetapoint3theta is ( ( angleattribution(s2thetapoint3X+singularity2X,s2thetapoint3Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2thetapoint3X+singularity2X,s2thetapoint3Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s2thetapoint4mover : step { auto layer, distance, clockwise, position; layer = 4; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s2thetapoint4theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) ##we do MINUS clockwise because things are mirrored s2thetapoint4t = ( (s2thetapoint4t - clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s2thetapoint4t ); s2thetapoint4X = -layer * (-22 + position % 360 ); s2thetapoint4Y = -layer * (-22 + (position - (position % 360)) / 360 ); } s2thetapoint4t = 0; s2thetapoint4theta is ( ( angleattribution(s2thetapoint4X+singularity2X,s2thetapoint4Y+singularity2Y,singularity1X,singularity1Y) - angleattribution(s2thetapoint4X+singularity2X,s2thetapoint4Y+singularity2Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s1thetapoint1mover : step { auto layer, distance, clockwise, position; layer = 1; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1thetapoint1theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1thetapoint1t = ( (s1thetapoint1t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1thetapoint1t ); s1thetapoint1X = layer * (-22 + position % 360 ); s1thetapoint1Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1thetapoint1t = 0; s1thetapoint1theta is ( ( angleattribution(s1thetapoint1X+singularity1X,s1thetapoint1Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1thetapoint1X+singularity1X,s1thetapoint1Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s1thetapoint2mover : step { auto layer, distance, clockwise, position; layer = 2; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1thetapoint2theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1thetapoint2t = ( (s1thetapoint2t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1thetapoint2t ); s1thetapoint2X = layer * (-22 + position % 360 ); s1thetapoint2Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1thetapoint2t = 0; s1thetapoint2theta is ( ( angleattribution(s1thetapoint2X+singularity1X,s1thetapoint2Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1thetapoint2X+singularity1X,s1thetapoint2Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s1thetapoint3mover : step { auto layer, distance, clockwise, position; layer = 3; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1thetapoint3theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1thetapoint3t = ( (s1thetapoint3t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1thetapoint3t ); s1thetapoint3X = layer * (-22 + position % 360 ); s1thetapoint3Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1thetapoint3t = 0; s1thetapoint3theta is ( ( angleattribution(s1thetapoint3X+singularity1X,s1thetapoint3Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1thetapoint3X+singularity1X,s1thetapoint3Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; proc s1thetapoint4mover : step { auto layer, distance, clockwise, position; layer = 4; clockwise = -1; ##work out if we want to go clockwise or anti. distance = s1thetapoint4theta - intendedtheta; if( distance > 90 || (distance < 0 && distance > -90) ) clockwise = 1; ##12 happens to be perimeter / distancebetweenlayers (which is 22) s1thetapoint4t = ( (s1thetapoint4t + clockwise) % (12 * 22) + (12 * 22) ) % (12 * 22); position = getXplus360y( s1thetapoint4t ); s1thetapoint4X = layer * (-22 + position % 360 ); s1thetapoint4Y = layer * (-22 + (position - (position % 360)) / 360 ); } s1thetapoint4t = 0; s1thetapoint4theta is ( ( angleattribution(s1thetapoint4X+singularity1X,s1thetapoint4Y+singularity1Y,singularity1X,singularity1Y) - angleattribution(s1thetapoint4X+singularity1X,s1thetapoint4Y+singularity1Y,singularity2X,singularity2Y) ) % 180 + 180 ) %180; s1thetaline1 is Line(singularity1X, singularity1Y, singularity1X+s1thetapoint1X,singularity1Y+s1thetapoint1Y, "White"); s1thetaline2 is Line(singularity1X+s1thetapoint1X,singularity1Y+s1thetapoint1Y, singularity1X+s1thetapoint2X,singularity1Y+s1thetapoint2Y, "White"); s1thetaline3 is Line(singularity1X+s1thetapoint2X,singularity1Y+s1thetapoint2Y, singularity1X+s1thetapoint3X,singularity1Y+s1thetapoint3Y, "White"); s1thetaline4 is Line(singularity1X+s1thetapoint3X,singularity1Y+s1thetapoint3Y, singularity1X+s1thetapoint4X,singularity1Y+s1thetapoint4Y, "White"); s2thetaline1 is Line(singularity2X, singularity2Y, singularity2X+s2thetapoint1X,singularity2Y+s2thetapoint1Y, "White"); s2thetaline2 is Line(singularity2X+s2thetapoint1X,singularity2Y+s2thetapoint1Y, singularity2X+s2thetapoint2X,singularity2Y+s2thetapoint2Y, "White"); s2thetaline3 is Line(singularity2X+s2thetapoint2X,singularity2Y+s2thetapoint2Y, singularity2X+s2thetapoint3X,singularity2Y+s2thetapoint3Y, "White"); s2thetaline4 is Line(singularity2X+s2thetapoint3X,singularity2Y+s2thetapoint3Y, singularity2X+s2thetapoint4X,singularity2Y+s2thetapoint4Y, "White"); s2philine1 is Line(singularity2X, singularity2Y, singularity2X+s2phipoint1X,singularity2Y+s2phipoint1Y, "Yellow"); s2philine2 is Line(singularity2X+s2phipoint1X,singularity2Y+s2phipoint1Y, singularity2X+s2phipoint2X,singularity2Y+s2phipoint2Y, "Yellow"); s2philine3 is Line(singularity2X+s2phipoint2X,singularity2Y+s2phipoint2Y, singularity2X+s2phipoint3X,singularity2Y+s2phipoint3Y, "Yellow"); s2philine4 is Line(singularity2X+s2phipoint3X,singularity2Y+s2phipoint3Y, singularity2X+s2phipoint4X,singularity2Y+s2phipoint4Y, "Yellow"); s1philine1 is Line(singularity1X, singularity1Y, singularity1X+s1phipoint1X,singularity1Y+s1phipoint1Y, "Yellow"); s1philine2 is Line(singularity1X+s1phipoint1X,singularity1Y+s1phipoint1Y, singularity1X+s1phipoint2X,singularity1Y+s1phipoint2Y, "Yellow"); s1philine3 is Line(singularity1X+s1phipoint2X,singularity1Y+s1phipoint2Y, singularity1X+s1phipoint3X,singularity1Y+s1phipoint3Y, "Yellow"); s1philine4 is Line(singularity1X+s1phipoint3X,singularity1Y+s1phipoint3Y, singularity1X+s1phipoint4X,singularity1Y+s1phipoint4Y, "Yellow"); ##ought to be that the albatross “skips” the 180 between left and right, if anything ##it’s “up to you” whether to add 180 to theta for albatross direction. ##These co ords are absolute and tiles are defined in relation AlbatrossX = 670; AlbatrossY = 670; Vel = 0.3; AlbatrossXvel is Vel * cos(phi+90); AlbatrossYvel is Vel * sin(phi+90); ##we have a single tile made of four, twice as big as the window. tileX is AlbatrossX - 90 - AlbatrossVirtualX; tileY is AlbatrossY - 90 - AlbatrossVirtualY; tile is Image("sky",tileX,tileY,360,360,"http://s24.postimg.org/6rynge4xx/bg360.png"); ##then you also have some white around the edges. The white can’t encroach, so this thing is small border is Image("whitewash",400,400, 540, 540, "http://s23.postimg.org/9wtj1bqcb/smallborder.png"); proc incrementor : step { after (1) { step++; } } AlbatrossVirtualX = 0; AlbatrossVirtualY = 0; ##THIS PART NEEDS TO BE COPYPASTED IN AGAIN proc Albatrossmover : step { AlbatrossVirtualX = ( AlbatrossVirtualX + AlbatrossXvel + 180) % 180; AlbatrossVirtualY = ( AlbatrossVirtualY + AlbatrossYvel + 180) % 180; } step = 0; albatrossimage is ( 0 <= theta && theta < 6 ) ? a30 : ( 6 <= theta && theta < 12 ) ? a31 : ( 12 <= theta && theta < 18 ) ? a32 : ( 18 <= theta && theta < 24 ) ? a33 : ( 24 <= theta && theta < 30 ) ? a34 : ( 30 <= theta && theta < 36 ) ? a35 : ( 36 <= theta && theta < 42 ) ? a36 : ( 42 <= theta && theta < 48 ) ? a37 : ( 48 <= theta && theta < 54 ) ? a38 : ( 54 <= theta && theta < 60 ) ? a39 : ( 60 <= theta && theta < 66 ) ? a40 : ( 66 <= theta && theta < 72 ) ? a41 : ( 72 <= theta && theta < 78 ) ? a42 : ( 78 <= theta && theta < 84 ) ? a43 : ( 84 <= theta && theta < 90 ) ? a44 : ( 90 <= theta && theta < 96 ) ? a45 : ( 96 <= theta && theta < 102 ) ? a46 : ( 102 <= theta && theta < 108 ) ? a47 : ( 108 <= theta && theta < 114 ) ? a48 : ( 114 <= theta && theta < 120 ) ? a49 : ( 120 <= theta && theta < 126 ) ? a50 : ( 126 <= theta && theta < 132 ) ? a51 : ( 132 <= theta && theta < 138 ) ? a52 : ( 138 <= theta && theta < 144 ) ? a53 : ( 144 <= theta && theta < 150 ) ? a54 : ( 150 <= theta && theta < 156 ) ? a55 : ( 156 <= theta && theta < 162 ) ? a56 : ( 162 <= theta && theta < 168 ) ? a57 : ( 168 <= theta && theta < 172 ) ? a58 : a59; a30 = Image("30",580,580,180,180,"http://s1.postimg.org/3vb497snf/alb30.png"); a31 = Image("31",580,580,180,180,"http://s1.postimg.org/ejjglss0b/alb31.png"); a32 = Image("32",580,580,180,180,"http://s1.postimg.org/8jvpi577v/alb32.png"); a33 = Image("33",580,580,180,180,"http://s1.postimg.org/9nftu3ruz/alb33.png"); a34 = Image("34",580,580,180,180,"http://s1.postimg.org/iwi0480qz/alb34.png"); a35 = Image("35",580,580,180,180,"http://s1.postimg.org/p3te4dwi3/alb35.png"); a36 = Image("36",580,580,180,180,"http://s1.postimg.org/atjtswg5n/alb36.png"); a37 = Image("37",580,580,180,180,"http://s1.postimg.org/lixil5ryj/alb37.png"); a38 = Image("38",580,580,180,180,"http://s1.postimg.org/7y6qm1c5n/alb38.png"); a39 = Image("39",580,580,180,180,"http://s1.postimg.org/eefpc4kp7/alb39.png"); a40 = Image("40",580,580,180,180,"http://s1.postimg.org/6crgu81xn/alb40.png"); a41 = Image("41",580,580,180,180,"http://s1.postimg.org/49ln0arij/alb41.png"); a42 = Image("42",580,580,180,180,"http://s1.postimg.org/8b2q5yjt7/alb42.png"); a43 = Image("43",580,580,180,180,"http://s1.postimg.org/pkj74k9mz/alb43.png"); a44 = Image("44",580,580,180,180,"http://s1.postimg.org/5v0ws41qj/alb44.png"); a45 = Image("45",580,580,180,180,"http://s1.postimg.org/apulqe023/alb45.png"); a46 = Image("46",580,580,180,180,"http://s1.postimg.org/77iltzz63/alb46.png"); a47 = Image("47",580,580,180,180,"http://s1.postimg.org/8qdzyz5qj/alb47.png"); a48 = Image("48",580,580,180,180,"http://s1.postimg.org/rjzsvz3yj/alb48.png"); a49 = Image("49",580,580,180,180,"http://s1.postimg.org/e4cs6ivgr/alb49.png"); a50 = Image("50",580,580,180,180,"http://s1.postimg.org/604o1s91n/alb50.png"); a51 = Image("51",580,580,180,180,"http://s1.postimg.org/bcy3tnmbv/alb51.png"); a52 = Image("52",580,580,180,180,"http://s1.postimg.org/67wwc19e3/alb52.png"); a53 = Image("53",580,580,180,180,"http://s1.postimg.org/hrx4qbt1n/alb53.png"); a54 = Image("54",580,580,180,180,"http://s1.postimg.org/gqww17c23/alb54.png"); a55 = Image("55",580,580,180,180,"http://s1.postimg.org/5slmj0ngr/alb55.png"); a56 = Image("56",580,580,180,180,"http://s1.postimg.org/qqrsh3nbf/alb56.png"); a57 = Image("57",580,580,180,180,"http://s1.postimg.org/ym2bvwwy3/alb57.png"); a58 = Image("58",580,580,180,180,"http://s1.postimg.org/gkj6y42x7/alb58.png"); a59 = Image("59",580,580,180,180,"http://s1.postimg.org/j34vysonf/alb59.png");