This was created using the following nodes :
The magic happens in the DynamicMathsExpression node group which was created using the Node Expressions add-on using the following expression text :
_x = Vector[x] , _y = Vector[y] , _z = Vector[z]
#The distance from origin after 1 turn of the spiral
_oneTurnDist = 1/Curviness{0.5}
_arms = floor(Arms{2})
#The distance of this 'point' from the origin
_pointRadialDist = (_x**2+_y**2)**0.5
#The angle to this point in relation to the origin
_pointAngle = atan2(_y,_x)+3.141593
#The proportion of this rotation
_pointTurn = _pointAngle / 2 / 3.141593
#The number of completed turns to get to the point distance
_completeTurns = floor((_pointRadialDist / _oneTurnDist - _pointTurn)*_arms)/_arms
#The number of spiral turns to get closed to this point (the two closest tracks)
_innerSpiralTurns = _completeTurns + _pointTurn
_outerSpiralTurns = _completeTurns + 1/_arms + _pointTurn
# The radial distance of this point on the spiral
_innerSpiralRadialDist = _innerSpiralTurns * _oneTurnDist
_outerSpiralRadialDist = _outerSpiralTurns * _oneTurnDist
#Set to 'true' if the 'inner' is closest - else 'outer' is closest
_innerSpiralClosest = abs(_pointRadialDist - _innerSpiralRadialDist) < abs(_pointRadialDist - _outerSpiralRadialDist)
#The distance from this point to the nearest point on the spiral on the z-plane.
_planarDistance = min(abs(_pointRadialDist - _innerSpiralRadialDist),abs(_pointRadialDist - _outerSpiralRadialDist))
#Calculate the distance to the point in 3d space (radial distance)
Distance = (_planarDistance**2+_z**2)**0.5
#How far along the spiral from the centre
Length = _innerSpiralClosest * _innerSpiralTurns + not(_innerSpiralClosest) * _outerSpiralTurns
Simply paste the above text into a new text block in the Text Editor and add an expression as ‘TEXT:<text_block_name>’ to generate the node group.
The same can be done with the free Node Expressions(Lite) add-on but requires a little more work as the sub-expressions need to be created manually. I’ve created a blend file with the groups and sub-groups already created which can be edited with the ‘lite’ version of the add-on or used without the add-on.
3dspiral.blend (764.0 KB)