Version 151216-1
Luis M Rosety Gil

DNA Helix

The DNA helix generated at Veleta is a mathematical double helix.

An helix can be expressed as the parametric function:

x = r·cos(t)
y = r·sin(t)
z = k·t

where t∈[0,2π)
z = k·2π → z increment after each turn.

Hence the nonparametric version (i.e. eliminitating t):

x = r·cos(k⋅z)
y = r·sin(k⋅z)

And therefore, both projections on the ZX or XY planes are simple sinusoid functions.

Translating the helix projection to the XY plane we get a simple sinusoid y = r⋅sin(k⋅x)

The second DNA helix can be seen as a second sinusoid with an angle shift:

y1 = r·sin(k⋅x)
y2 = r·sin(k⋅x + x0;)

where x0 ∈[0,2π] ≡ Second helix shift

Changing these parameters allows customising the DNA helix shape.