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Doing a cyclic permutation on the sequence results in a rotation of the pattern by 90 degrees.

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In the sequence, multiples of 4 did not allow for the loop to return to it's original starting point.

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I understand that when the loop has 4 numbers, it must be lengths that describe a square or rectangle to close. 

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I understand that when the loop has 4 numbers, it must be lengths that describe a square or rectangle to close. 

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For the most part, an odd number of numbers will bring you back to the starting point, and an even number of numbers will not.

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For the most part, an odd number of numbers will bring you back to the starting point, and an even number of numbers will not.

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We noticed a 1, 2, 3, ___ pattern always was infinite

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We noticed a 1, 2, 3, ___ pattern always was infinite

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The role the sequence of numbers play when determining if the spiral will go off the page to the top right or bottom left.

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The role the sequence of numbers play when determining if the spiral will go off the page to the top right or bottom left.

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I understand that I know nothing yet.

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the number of turns is important, if you have 4 turns or a multiple of 4 turns a spiral is created, the others will form a loop that returns to the start

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the number of turns is important, if you have 4 turns or a multiple of 4 turns a spiral is created, the others will form a loop that returns to the start

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Relations between this activity and making predictions to movements on a coordinate plane.

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Relations between this activity and making predictions to movements on a coordinate plane.

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The chosen numbers determine the shape.  Negative numbers are on the bottom of the grid and positive numbers at the top.  The amount of numbers selected also changes the shape.

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The chosen numbers determine the shape.  Negative numbers are on the bottom of the grid and positive numbers at the top.  The amount of numbers selected also changes the shape.

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I understand that the loop does not always come back to its original starting point, and that when there are four numbers or a multiple of four numbers in a sequence, the pattern instead goes off the page.

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I understand that the loop does not always come back to its original starting point, and that when there are four numbers or a multiple of four numbers in a sequence, the pattern instead goes off the page.

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I wonder how adding a longer sequence in affects the shape of the loop de loops.

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I wonder how adding a longer sequence in affects the shape of the loop de loops.

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Are there different formulas to follow for different results.

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Are there different formulas to follow for different results.

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what combos of numbers spiral, which ones don't

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what combos of numbers spiral, which ones don't

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Is it always the same number of loops before it comes back to the starting point?

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Is it always the same number of loops before it comes back to the starting point?

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sometimes they spiral back to the start, sometimes they go off the page

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sometimes they spiral back to the start, sometimes they go off the page

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Do they always loop back to the original point in a specific number of loops?

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Do they always loop back to the original point in a specific number of loops?

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I noticed that there seemed to be some loopde loops where rectangles sat next to each other, some that looked open (rectangles far from the center) and some wer overlapping (the bigger sides were overlapping)

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I noticed that there seemed to be some loopde loops where rectangles sat next to each other, some that looked open (rectangles far from the center) and some wer overlapping (the bigger sides were overlapping)

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I noticed 2, 3, 4,4,4,3,6,6,1 made a cool pattern

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The numbers represented the line lengths

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I wonder what numbers make close figures and what numbers make 'open' figures.

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I wonder what numbers make close figures and what numbers make 'open' figures.

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I wonder if the spirals that leave the page actually come back

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I wonder if the spirals that leave the page actually come back

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What causes some to come back and others to go off infinitely?  Do all of the ones that come back to themselves, do it in 4 loops?

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What causes some to come back and others to go off infinitely?  Do all of the ones that come back to themselves, do it in 4 loops?

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at four numbers descending the spiral leaves the page and does not appear to come back 

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at four numbers descending the spiral leaves the page and does not appear to come back 

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some spiral off, others come back around

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some spiral off, others come back around

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The order of the (same group of) numbers can change the direction of the loop/figure.

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The order of the (same group of) numbers can change the direction of the loop/figure.

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The numbers represented the line lengths

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The numbers represented the line lengths

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I wondered if even numbers of moves would always move away.

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What makes a sequence return to its origin?

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What makes a sequence return to its origin?

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Some number combos looped over the center point and some looped around the center point.

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Some number combos looped over the center point and some looped around the center point.

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The numbers all greated loops, some were closed and others no. I didn't expect the non-closed loops.

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The numbers all greated loops, some were closed and others no. I didn't expect the non-closed loops.

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I wonder what is the biggest numbers you can select to make the largest loops that return back to the original point.

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I wonder what is the biggest numbers you can select to make the largest loops that return back to the original point.

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The lines always cross over each other in the examples

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The lines always cross over each other in the examples

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How are the chosen numbers related to the grid?

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How are the chosen numbers related to the grid?

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I noticed that the loop always came back around to meet the starting point after 

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I noticed that the loop always came back around to meet the starting point after 

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I noticed that some numbers loop back to the original point. 

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I noticed that some numbers loop back to the original point. 

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Bigger spread of numbers created larger rectangles.

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Bigger spread of numbers created larger rectangles.

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Odd numbers of moves seemed to connect.