mathematics - Welcome to Oɴᴇderland

                                                    1 1
                                                  1 1 1 1
                                                1 1 1 1
                                1             1 1 1 1
                                1           1 1 1 1
                                1 1 1     1 1 1 1
                                1 1 1 1 1 1 1 1
                                1 1 1 1 1 1 1
                                1 1 1 1 1 1
                                1 1 1 1 1 1 1 1

                                1 1 1 1 1 1 1 1 1 1

         #1.   You are here

            1111111111111111111111111111111
            111                         111
            111   1111111111111111111   111111111111111111111111111
            111   111             111   111                     111
            111   111   1111111   111   111   111111111111111   111

            111   111       111   111   111   111         111   111
            111   1111111   111   111   111   111   111   111   111
            111             111   111   111         111   111   111
            1111111111111111111   111   111111111111111   111   111
                                  111                     111   111
                      111111111111111111111111111111111111111   111
                      111                                       111
                      111   111111111111111111111111111111111111111
                      111   111
                      111   111   111111111111111

                      111   111   111         111
                      111   111   111   111   111
                      111   111         111   111
                      111   111111111111111   111
                      111                     111
                      111111111111111111111111111

         #2.   Through the labyrinth we wind

                           1ooo11ooo1
                       111ooooo1   1oo111o
                       1 oo1111   1      1
                       o1   o1   1        1
                      o1    1   1          1
                       o1   1   1           1
                        1    1   1          1
                         1    1   11ooo1oo1o111oo
                          1ooo11o1     oooo1
                          o1 1111  ooo1111

                         1111    1111111
                         1          1111
                                     1111
                                       o1
                                       o1
                                o1111   o1
                             oo1     o1 o1
                            o1         1111
                           o1      ooo1oo111o
                           1   ooo1      o1

                           1111           1
                            1

         #3.   A rose is a rose is a rose

                                                1
                                               1 1
                                              1o1o1
                                             1 1 1 1

                                    1       1o1o1o1o1       1
                                   1 1     1 1     1 1     1 1
                                  1o1o1   1o1o1   1o1o1   1o1o1
                                 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
                                1o1o1o1o1o1o1o1o1o1o1o1o1o1o1o1o1
                               1 1     1 1             1 1     1 1
                              1o1o1   1o1o1           1o1o1   1o1o1
                             1 1 1 1 1 1 1 1         1 1 1 1 1 1 1 1
                            1o1o1o1o1o1o1o1o1       1o1o1o1o1o1o1o1o1
                           1 1             1 1     1 1     1 1

                          1o1o1           1o1o1   1o1o1   1o1o1
                         1 1 1 1         1 1 1 1 1 1 1 1 1 1 1 1
                        1o1o1o1o1       1o1o1o1o1o1o1o1o1o1o1o1o1
                       1 1     1 1     1 1     1 1
                      1o1o1   1o1o1   1o1o1   1o1o1
                     1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
                    1o1o1o1o1o1o1o1o1o1o1o1o1o1o1o1o1

         #4.   $\sf \small O \scriptsize NE$ders of the ancient world

Obviously (?) the $\sf\scriptsize ZERO$-and$\small/$or-$\sf\scriptsize ONE$ders here represent a pattern of mathematical constructs.

                                            o?1?o?1?
                                           1?      o?
                                                   1?
                                                  o?
                                                1?
                                               o?

                                               1?

         #5.   What picture could be fifth, but not at other #s here?     Why?

                                                               1o111111ooooo
                                                         oooooo1o11111ooooo
                                                   oooooooooooo1o1111ooooo
                                             oooooooooooooooooo1o111ooooo
                                       oooooooooooooooooooooooo1o11ooooo
                                 oooooooooooooooooooooooooooooo1o1ooooo

                           ooooooooooooooooooooooooooooooooooo11o1oooo
                     oooooooooooooooooooooooooooooooooooooooo111o1ooo
               ooooooooooooooooooooooooooooooooooooooooooooo1111o1oo
         oooooooooooooooooooooooooooooooooooooooooooooooooo11111o1o
   ooooooooooooooooooooooooooooooooooooooooooooooooooooooo111111o1

         #6.   One for the road

The answer can be pictured in infinitely many ways. The ?-shaped placeholder presently at #5 is meant to be replaced. Only numbers composed of o zeros and$\small/$or 1 ones are pertinent. Two-dimensional shapes and surrounding words are just gratuitous embellishments. If you’re getting nowhere after considering all this, why not actually go nowhere, to $\sf \small N \scriptsize ONE$derland, for comparison?

Answer

In the $n$th picture, the strings are all

representations of the number $1$ where the base is one of the primitive $n$th roots of unity. (That is, solutions to $z^n=1$ that don't work for any smaller $n$.)

So any picture containing

111111

would fit in slot 5, but not any other.