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The Pell number sequence starts with 0 and 1. Each number is generated by doubling the previous number in sequence and adding it to the one before (Pn = 2Pn-1 + Pn-2). The first ten numbers in the sequence are 0, 1, 2, 5, 12, 29, 70, 169, 408, 980. Recently, I have been generating and drawing trees that represents a number in this sequence by its number of nodes (which can also be called leaves or fruit).
Each tree represents a Pell number from 5 to 408.
Pell Forest in Sequence
Pell Forest in Sequence
A more organized take on representing Pell numbers using trees.
No random numbers are used here.
Four Point Pell Snowflake
Four Point Pell Snowflake
Made by rotating four 408 node Pell trees around a point. This piece was drawn with a digital pen on Goodnotes.
The slight imperfections in spacing mirror the natural irregularities of real snowflakes coincidentally.
Pell Flower
Pell Flower
Similar to the Pell Snowflake this piece uses four 70 node Pell trees that rotate around a point. The colors and shape make it appear more of a flower than a snowflake.
This piece was created using draw.io.
408 Node Pell Tree
408 Node Pell Tree
408 is the ninth Pell number and comes from the seventh and eighth Pell numbers (70 and 169 with 70 + 2(169) =408). This tree is built from a 70 node pell tree at the bottom and two 169 at the top.
When I first made a 408 tree I was suprised by how it resembles a Sierpiński triangle
408 Node Pell Tree Using Random Numbers
408 Node Pell Tree Using Random Numbers
This tree was purposely adjusted to look like a tree with longer branches and a shorter trunk.
408 Node Pell Tree Using Random Numbers
408 Node Pell Tree Using Random Numbers
A sample from when I started using random numbers to create a more natural looking tree.
Pell Forest in Sequence
Pell Forest in Sequence
These trees go from left to right representing five Pell numbers(5, 12, 29, 70, and 169).
The random numbers started to spread out the leaves more here.
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