螺旋方形网格序列
Grid Versions (ninja turtle ;-)
Grid_{Iteration}=Element(Transpose(IterationList({Element(σ, 1) + Vector(Element(Moves, x(Element(σ, 2)))), (x(Element(σ, 2)) + 1, 0)}, σ, {{(0, 0), (1, 0)}}, (n + 1) (n + 2))), 1)
Grid=Flatten({{(0, 0)}, Sequence(Sum(Take(Moves, 1, j)), j, 1, Length(Moves))})
Grid berechnet für jeden neuen Punkt die gesamte Folge vom Start ab beginnend neu!
Grid recalculates the entire sequence from the start for each new point
20260719 修改自：hawe — 2024年4月5日 - 上午4:31的 Spirali-Square-Grid – GeoGebra
#基本向量，一步一个单位
R = {(0, 1), (-1, 0), (0, -1), (1, 0)}
n = 4
#每一步的方向
Moves=扁平列表(序列({序列(元素(R, 余式(2k, 4) + 1), j, 0, k), 序列(元素(R, 1 + 余式(2k + 1, 4)), j, 0, k)}, k, 0, n))
#Moves = {(0, 1), (-1, 0), (0, -1), (0, -1), (1, 0), (1, 0), (0, 1), (0, 1), (0, 1), (-1, 0), (-1, 0), (-1, 0), (0, -1), (0, -1), (0, -1), (0, -1), (1, 0), (1, 0), (1, 0), (1, 0), (0, 1), (0, 1), (0, 1), (0, 1), (0, 1), (-1, 0), (-1, 0), (-1, 0), (-1, 0), (-1, 0)}
#点阵
Grid=扁平列表({{(0, 0)}, 序列(总和(提取(Moves, 1, j)), j, 1, 长度(Moves))})
#Grid = {(0, 0), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (1, -1), (1, 0), (1, 1), (1, 2), (0, 2), (-1, 2), (-2, 2), (-2, 1), (-2, 0), (-2, -1), (-2, -2), (-1, -2), (0, -2), (1, -2), (2, -2), (2, -1), (2, 0), (2, 1), (2, 2), (2, 3), (1, 3), (0, 3), (-1, 3), (-2, 3), (-3, 3)}
#路径
Spirali 折线(Grid)
text1="an = (n+1)(n+2) = a" + n + " = " + (n + 1) + " * " + (n + 2) + " = " + ((n + 1) (n + 2)) + "" "a_n = (n+1)(n+2) = a_{4} = 5 * 6 = 30"
#点阵，与Grid等价
GridIteration=元素(转置(迭代列表({元素(σ, 1) + 向量(元素(Moves, x(元素(σ, 2)))), (x(元素(σ, 2)) + 1, 0)}, σ, {{(0, 0), (1, 0)}}, (n + 1) (n + 2))), 1)
#GridIteration = {(0, 0), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (1, -1), (1, 0), (1, 1), (1, 2), (0, 2), (-1, 2), (-2, 2), (-2, 1), (-2, 0), (-2, -1), (-2, -2), (-1, -2), (0, -2), (1, -2), (2, -2), (2, -1), (2, 0), (2, 1), (2, 2), (2, 3), (1, 3), (0, 3), (-1, 3), (-2, 3), (-3, 3)}
goTurtle = true
更新时
如果(goTurtle,执行({"T=Turtle()","StartAnimation(T,true)"}),执行({"StartAnimation(T,false)","Delete(T)"}))
如果(goTurtle,执行(RunTurtle))
#海龟行走脚本
RunTurtle=扁平列表(序列({"TurtleLeft(T, 90°)", "TurtleForward(T," + (k) + ")", "TurtleLeft(T, 90°)", "TurtleForward(T," + (k) + ")"}, k, 1, n + 1))
#RunTurtle = { TurtleLeft(T, 90 ) , TurtleForward(T,1) , TurtleLeft(T, 90 ) , TurtleForward(T,1) , TurtleLeft(T, 90 ) , TurtleForward(T,2) , TurtleLeft(T, 90 ) , TurtleForward(T,2) , TurtleLeft(T, 90 ) , TurtleForward(T,3) , TurtleLeft(T, 90 ) , TurtleForward(T,3) , TurtleLeft(T, 90 ) , TurtleForward(T,4) , TurtleLeft(T, 90 ) , TurtleForward(T,4) , TurtleLeft(T, 90 ) , TurtleForward(T,5) , TurtleLeft(T, 90 ) , TurtleForward(T,5) }
T=海龟() T = null
, text2 "https://www.geogebra.org/geometry?command=R%3D%7B%280%2C1%29%2C%28-1%2C0%29%2C%280%2C-1%29%2C%281%2C0%29%7D%3Bn%3DSlider%280%2C99%2C1%2C1%2C200%2Cfalse%2Ctrue%2Cfalse%2Cfalse%29%3BPK%3DFlatten%28Sequence%28%7BSequence%28Element%28R%2CMod%282k%2C4%29%2B1%29%2Cj%2C0%2Ck%29%2CSequence%28Element%28R%2C1%2BMod%282k%2B1%2C4%29%29%2Cj%2C0%2Ck%29%7D%2Ck%2C0%2Cn%29%29%3BSPIRALI%3DFlatten%28%7B%7B%280%2C0%29%7D%2CSequence%28Sum%28Take%28PK%2C1%2Cj%29%29%2Cj%2C1%2CLength%28PK%29%29%7D%29%3BPolyline%28SPIRALI%29"
, text3 "https://www.reddit.com/r/geogebra/comments/1buxucx/sequence/"