Output a binary path from a number

MATL, 14 bytes

J_iB^YsJ+'o-'&XG

Produces graphical output as a path starting at coordinates (0,0). Try it at MATL Online! Or see some offline examples below:

• Input 7:

  

  Output:

  

• Input 699050:

  

  Output:

  

If you prefer, you can see the path as complex coordinates for 9 bytes:

J_iB^YsJ+

Try it online!

Explanation

J_      % Push -1j (minus imaginary unit)
i       % Push input number
B       % Convert to binary. Gives an array of 0 and 1 digits
^       % Power, element-wise. A 0 digit gives 1, a 1 digit gives -1j
Ys      % Cumulative sum. Produces the path in the complex plane
J+      % Add 1j, element-wise. This makes the complex path start at 0
'o-'    % Push this string, which defines plot makers
&XG     % Plot

MATL, 10 bytes

YsG~YsQ1Z?

Inputs an array of binary digits. Outputs a matrix.

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Explanation

Ys    % Implicit input: array of binary digits. Cumulative sum. This gives the
      % row coordinates
G     % Push input again
~     % Negate: change 0 to 1 and 1 to 0
Ys    % Cumulative sum
Q     % Add 1. This gives the column coordinates
1Z?   % Matrix containing 1 at those row and column coordinates and 0 otherwise.
      % Implicit display

Jelly, 8 bytes

¬œṗ+\Ṭz0

A monadic link accepting a number as a list of ones and zeros (e.g. 13 is [1,1,0,1]) returning a list of lists of ones and zeros where the first list is the first row.

Try it online! or see a formatted test-suite

How?

¬œṗ+\Ṭz0 - Link: list L           e.g. [1,1,0,0,1,1,0,1] (i.e. 205)
¬        - logical NOT L               [0,0,1,1,0,0,1,0]
    \    - cumulative reduce L by:
   +     -   addition                  [1,2,2,2,3,4,4,5]
 œṗ      - partition @ truthy indices  [[1,2],[2],[2,3,4],[4,5]]
     Ṭ   - un-truth (vectorises)       [[1,1],[0,1],[0,1,1,1],[0,0,0,1,1]]
      z0 - transpose with filler 0     [[1,0,0,0],[1,1,1,0],[0,0,1,0],[0,0,1,1],[0,0,0,1]]
         -                        i.e.  1000
                                        1110
                                        0010
                                        0011
                                        0001