New Solution

Draw a straight line across the paper so as to have a vertical and horizontal axis. Move the compass to the centre of the line and scribe a circle. Move the compass to x+radius and scribe a second circle. Then to x-radius and scribe a third. Where the circles intersect, draw the displayed red lines. These divide the radius into four. The next step is to create more circles to enable a grid to be created.

This step is the drawing of more circles, using the same method, to enable a grid to be created. Move the compass from x+2*r through x-2*r, and the same along the y axis. Then for the new process this needs to be extended to x and y times eight. When the points of intersection of the circles are joined together, a grid is formed dividing the radius into four, i.e. the x and y axis into fourteen because we are now including the triangle with a base of fourteen times 'g'.

Having drawn a line across the paper and carried out the circle drawing steps create the grid by drawing lines through the points of intersection of the circles. Each square so formed has sides equal to one quarter of the radius, regardless of the length of the radius.

Using your rule, draw a line from x-4*g/y-3*g through x-1*g/y-2*g through x+2*g/y-1*g to the edge of the grid. The graphic does not show the lines to the edge of the grid. . Draw a line from the centre of the cross through the radius where it intersects the circle, to the edge of the grid.