EulerBeats Genesis

Genesis Originals

EulerBeats Genesis originals are ultra scarce NFTs and are capped at 27. The token seed was generated on-chain at the time of creation. The user’s wallet address, the block hash were part of inputs into the seed and token generation process. This means the buyer of the original token was not able to preview the art + beat and had to wait to see the result after the token was minted. The 27 EulerBeats originals were all priced at 0.271 Ξ + gas.

Buying Genesis Prints

The pricing of the Genesis prints and the redemption value of the burned print are set on the bonding curve described below. The burn prices vary based on the current supply. A print token burn yields 90% of the cost of printing the nth print. Burning reduces the current supply to n - 1. For the Genesis print tokens, a user must first approve the request to burn and then perform the actual burn of the token. The request approval only needs to be done once.

Genesis Bonding Curve

There is a bonding curve that prices the print for each original based on the function:

f(x) = a(b+x) + cx + d

where x denotes the current print supply + 1 and

a = 1.1

b = -50

c = 0.026

d = -0.008

90% of the print price is stored in a reserve to refund burned prints. The remaining 8% is sent to the Original holder and 2% goes to the EulerBeats project.

Genesis Art + Music Generation

The art and music generation of every EulerBeat original is guaranteed to be unique. The art is based on Euler's totient function Phi (ɸ) that counts the positive integers up to a given integer n that are relatively prime to n. In a grid-like arrangement, cells are filled with colored shapes if the row and column the cell represents are co-prime to each other.

The art has the following traits

  • Grid Size: Ranges from being a 7x7 to a 12x12 symmetrical matrix.

  • Diagonal Lever: This is a combined lever that shifts both the horizontal (X) and vertical (Y) viewing window of the typical Euler's totient Phi (ɸ) graph.

  • Horizontal Lever: This lever shifts the viewing window of the typical Euler's totient Phi (ɸ) graph horizontally in addition to the diagonal lever.

  • These levers help to produce interesting view patterns and also eliminates some edge conditions like an empty area.

  • Color Palette: This determines the color of the cells and the color of the shape that decorate the cells.

  • Shape: There are 4 shapes that render the cells that are relatively prime to the rows and columns they represent. The shapes used to render each cell represent the rarity.

While EulerBeats original is guaranteed to be unique, the probability of generating the particular shape is as follows: circle (70%), square (10%), square circle (10%), square diamond (10%).

The coprimes matrix is used as input to generate the rhythmic base. The first bottom rows and last column are assigned to different percussion instruments. The dynamic accent comes from the count of coprimes in each column and row (a partial totient function of sorts) at every beat, so beat intensity is higher for prime numbers. The token seed is used to randomly generate chord progressions and melodies using our simple but effective music theory engine.

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