Cut and paste each of these lines of code into the Input bar. You may need to tweak slightly depending which version of GeoGebra you use. For the talk I will be using https://www.geogebra.org/classic
The one that started it all:
Sequence(Translate(Sequence(Translate(Polygon((0, 0), (1, 0), 4), Vector((0, 0), (k, ((-1)^(k – 1) + 1) / 2))), k, 0, 7), (0, 2m)), m, 0, 3)
Polygon(Sequence(Rotate((0,1),144°*k),k,0,4))
Polygon(Sequence(Rotate((0,1),((360)/(a)) ((a+1)/(2))° k),k,0,a-1))
Sequence(Enlarge(Polygon((1, 0), (1, 2),(0,2),(0,0),(2,0),(2,1),(1,1)),0.5^k,(2,2)),k,0,10)
Sequence(Dilate(Polygon((1, 0), (1, 2),(0,2),(0,0),(2,0),(2,1),(1,1)),0.5^k,(2,2)),k,0,10) if you’re using the web version)
And some one-liners: https://www.geogebra.org/m/rdatunjf
More elaborate one-liners that took more than one line https://www.geogebra.org/m/papc4dth
Update: Finally got the Fibonacci square tiling pattern working, a week after my Mathsjam talk. It’s one line, but quite a long line… Sequence(Polygon((Sum(Sequence((-1)^(floor(((n)/(2)))) ((((0.5+0.5 sqrt(5))^(n-1)-(0.5-0.5 sqrt(5))^(n-1))/(sqrt(5))) ((1+(-1)^(n))/(2))+(((0.5+0.5 sqrt(5))^(n+2)-(0.5-0.5 sqrt(5))^(n+2))/(sqrt(5))) ((1-(-1)^(n))/(2))),n,1,k))-(((0.5+0.5 sqrt(5))^(k+1)-(0.5-0.5 sqrt(5))^(k+1))/(sqrt(5))),Sum(Sequence((-1)^(floor(((n-1)/(2)))) ((((0.5+0.5 sqrt(5))^(n+2)-(0.5-0.5 sqrt(5))^(n+2))/(sqrt(5))) ((1+(-1)^(n))/(2))+(((0.5+0.5 sqrt(5))^(n-1)-(0.5-0.5 sqrt(5))^(n-1))/(sqrt(5))) ((1-(-1)^(n))/(2))),n,1,k))-(((0.5+0.5 sqrt(5))^(k+1)-(0.5-0.5 sqrt(5))^(k+1))/(sqrt(5)))),(Sum(Sequence((-1)^(floor(((n)/(2)))) ((((0.5+0.5 sqrt(5))^(n-1)-(0.5-0.5 sqrt(5))^(n-1))/(sqrt(5))) ((1+(-1)^(n))/(2))+(((0.5+0.5 sqrt(5))^(n+2)-(0.5-0.5 sqrt(5))^(n+2))/(sqrt(5))) ((1-(-1)^(n))/(2))),n,1,k))+(((0.5+0.5 sqrt(5))^(k+1)-(0.5-0.5 sqrt(5))^(k+1))/(sqrt(5))),Sum(Sequence((-1)^(floor(((n-1)/(2)))) ((((0.5+0.5 sqrt(5))^(n+2)-(0.5-0.5 sqrt(5))^(n+2))/(sqrt(5))) ((1+(-1)^(n))/(2))+(((0.5+0.5 sqrt(5))^(n-1)-(0.5-0.5 sqrt(5))^(n-1))/(sqrt(5))) ((1-(-1)^(n))/(2))),n,1,k))-(((0.5+0.5 sqrt(5))^(k+1)-(0.5-0.5 sqrt(5))^(k+1))/(sqrt(5)))),4),k,0,19)
Had a go at Truchet Tiles: Sequence(Translate(Sequence(Translate(Rotate({CircularArc((0, 0), (0.5, 0), (0, 0.5)), CircularArc((1, 1), (0.5, 1), (1, 0.5))}, RandomBetween(0, 3) * 90°, (0.5, 0.5)), (k, 0)), k, 0, 50), (0, m)), m, 0, 50)