Spirangles

[fairyrak]

Well I know that I can more or less walk in a spiral without accessories by doing this:

1 step east, 1 step south, 2 steps west, 2 steps north, 3 steps east, 3 steps south, 4 west, 4 north etc but that means that I'd have to walk in angles of 90 degrees all the time.

If I change the angles to 45, how can I calculate the number of steps?
And what if I instead of that i change the 90 or 45 degrees to a generic n angle whatever between 1 to 359 degrees?

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(this was for fun, to explore the terrain of the game skyrim efficiently (without missing a lot of places) but it could be useful for other purposes too, like having an extreme fun in discovering or visiting or exploring the shops of the blocks of a city (because the angles of the blocks are 90 in my city

[Old_Geezer]

Unsure what equation(s) you need, but in your shoes I'd arm myself with a large sheet of paper, pencil, ruler, and set square/protractor, and see what distances and distance change rules, work.

[Peter Pedant]

spirals definitely
I remember being fascinated by this ssort of thing
but then being told the math was too complicated for me

I am pretty sure it is an 'equiangular spiral' coz kind of all your angles are equal

and if you goggle equiangular spiral
alot comes up like this
http://www.intmath.com/plane-analytic-geometry/equiangular-spiral.php

of varying degrees ( ha!) of difficulty

It is a big thing in biology - not noted mathematicians so there has to be simpler non math treatments of the subject out there