Parallel exponentially expanding lines

[ordreams]

Hi,

I have a question that relates to maths in art.

I require sets of say five parallel lines that expand exponentially. The issue I have, though, is that I want to maintain the same relationships of the ratio of expansion across different distances. (sorry if not the technically correct description). How can I calculate this?

I did a dodgy picture to try to help illustrate.

Thanks in advance.

 

[Dr.Peterson]

Like this?



Just make one, and then expand or contract proportionally (that is, multiply all distances by the same number). Here, I made the middle one using distances 1, 2, 4, 8, copied that left and right, and stretched and compressed respectively. If the left one is 1.27 times the original, then multiply all vertical distances by 1.27.

 

[ordreams]

That´s great!

That is really easy and clear.

I think that what I was more trying to do was calculate backwards. For example; if I start at 100 with subdivisions, and 70 same proportions of subdivisions, and 20, etc. - calculating the lengths of the expanding parts within each length.

Thanks

 

[HallsofIvy]

What, exactly, does "exponentially expanding" mean? Do you, as Dr. Peterson is assuming, mean that the distance between the lines increases exponentially?

 

[ordreams]

Hi, sorry for the slow reply.

I think the idea of ratios based on some basic drawing is easiest, but I would be happy to know how to calculate how to get the same exponent of expansion at different lengths of line.