Using Euclidean Distances

"The Plot Thickens"

SELF When investigating various Standards of Perfection and how they relate to actual varieties of auricula an objective method for mapping them is needed.
The technique chosen Euclidean Distances is just an extension of the familair Pythagoras Theorem into extra dimensions.


SELF To do this measure, interpret or calculate the percentage of the radius occupied by each part. In practice it is easier to measure the diameter of the concentric circles and then compute the desired values. The illustrations describe how this is done for three parts or zones (the edge including the ground, the eye or paste and the tube).

ALPINE Plot this data in multiple dimension space (in the example on the right 3D). All the flat flowered auriculas including selfs, edges, fancies, stripes and aplines have three parts (edge, eye and tube). Some have patterns in the edge (and all have potentially patterns created by the anthers within the tube) that approximate to further concentric circles which could be represented using additional dimensions.


STRIPE This can be simplified (to 2D in the example) with a change in scale and use of non-rectilinear Cartesian coordinates. On this map particular flowers can be plotted and lines of equal ratio E/e=1.5 (see below) or proportion E/e=e/t (not shown) can be graphed.

florist standards

florist reference points Here on the left we have a close-up map of the florist standards with the addition of a plot of the average of winning edged plants (1958-61) observed by Bond.

Once the three florist standards are mapped, Bond could be plotted using Euclidean distances and triangulation.
Grid lines like latitude and longitude can be drawn for incremental values of E/C and e/t respectively.

Now theoretical cases and varieties can be easily plotted using the values derived from actual plants or photographs.

C1, C2 and C3 are cases from the page about Continuous Proportions.
In 3D case C3 in the same as Glenny.
Edged auriculas
Edged auriculas
Self auriculas
Self auriculas
Alpine auriculas
Alpine auriculas
The Dominant Ratio R is 1.414 (root 2) although Phi is also in evidence.

The patterns (e::2t::e) for the centre approximate to 1::R::1 1::R2::1 1::(R+1)::1

The E/e ratios approximate to
R for white edges,
Phi(1.618) or R2 for grey edges
and R2 or R+1 for green edges.
For selfs it is difficult to judge whether Phi or root 2 dominates. Root 2 dominates.

The pattern (e::2t::e) for the centre approximates to 1::R::1
which equates to 1::R-1::R-1::1,
a powerful continuous proportion can be seen.

The E/e ratios approximate to
R, R-1+1, R2 and R2+1.
For people using Internet Explorer the graphs below can be clicked on and dragged as overlays to the maps above.
Some lines of continuous proportion
Root 2 based
Some Root 2 based ratios
Phi based
Some Phi based ratios