💫{n} dimensions
Understanding the dimensions of data representation
In the realm of data representation, dimensions play a critical role in how we structure, interpret, and utilize information. The concept of dimensionality is foundational, spanning from one-dimensional (1D) arrays, where data is linear and sequential, through two-dimensional (2D) matrices that offer a tabular view of information, to three-dimensional (3D) models that provide spatial representation.
1D (One-Dimensional)
In 1D data representation, data is organized linearly, akin to a list or array. Each element has a single value and is accessed by a single index, making it straightforward for operations like search and sort. This simplicity is foundational, serving as the building block for more complex structures.
2D (Two-Dimensional)
Expanding to 2D, data is arranged in rows and columns, much like a matrix or table. This facilitates more complex relationships, enabling operations that require context across two axes, such as in spreadsheet calculations or pixel-based image processing. It's a critical step up in representing relational and spatial data.
3D (Three-Dimensional)
With 3D data representation, we add depth to our spatial structuring, allowing for models and simulations that mirror real-world complexities. Each data point in this space is defined by three coordinates. This dimension is pivotal in fields requiring volumetric representations, from computer graphics to medical imaging, offering an immersive perspective on data.
Each step up in dimensionality enriches our ability to represent and interact with data, opening new avenues for analysis, visualization, and application across diverse computational fields.
What is {n} dimensions
Through the lens of the principles above we can visualise Bitcoin's blockchain in the same light. Consider the following:
1D | The block heights
2D | The block properties (header) and the transactions
3D | Header values and transaction values
4D | Specific input or output
5D | Output or input value
6D | Input or output array value
Let's look at an example with a simple block like Block 170. Below is the available data.
Block Header
The block header is the first element of data in every block and contains the properties of the block. It is the data displayed for individual blocks when viewing on blockchain explorers.
const header = [
170, // height
1960, // weight
490, // size
490, // strippedsize
1889418792, // nonce
2, // ntx
"00000000d1145790a8694403d4063f323d499e655c83426834d4ce2f8dd4a2ee", // blockhash
"0x1", // version
"1", // versionhex
"7dac2c5666815c17a3b36427de37bb9d2e2c5ccec3f8633eb91a4205cb4c10ff", // merkleroot
"0x1d00ffff", // bits
"000000000000000000000000000000000000000000000000000000ab00ab00ab", // chainwork
"1.00", // difficulty
"2009-01-12 03:30:25", // time
"Jan 11, 2009 23:24:05 UTC" // mediantime
];Transactions
Transaction data makes up the rest of the block. Here you will find all the information about individual transactions including inputs and outputs.
const tx0 = [
134, // size
134, // vzize
536, // weight
1, // version
"b1fea52486ce0c62bb442b530a3f0132b826c74e473d1f2c220bfa78111c5082", // txid
true, // coinbase
000000000, // btcfee
0, // locktime
"12 Jan 2009 03:30:25", // blocktime
[[ // inputs
"0000000000000000000000000000000000000000000000000000000000000000", // txid
4294967295, // output
"04ffff001d0102", // sigscript
4294967295, // sequence
null, // pkscript
null, // value
null, // address
[] // witness
]],
[[ // outputs
"1PSSGeFHDnKNxiEyFrD1wcEaHr9hrQDDWc", // address
"4104d46c4968bde02899d2aa0963367c7a6ce34eec332b32e42e5f3407e052d64ac625da6f0718e7b302140434bd725706957c092db53805b821a85b23a7ac61725bac", // pkscript
5000000000, // value
false, // spent
null // spender
]]
];const tx1 = [
275, // size
275, // vzize
1100, // weight
1, // version
"f4184fc596403b9d638783cf57adfe4c75c605f6356fbc91338530e9831e9e16", // txid
false, // coinbase
000000000, // btcfee
0, // locktime
"12 Jan 2009 03:30:25", // blocktime
[[ // inputs
"0437cd7f8525ceed2324359c2d0ba26006d92d856a9c20fa0241106ee5a597c9", // txid
0, // output
"47304402204e45e16932b8af514961a1d3a1a25fdf3f4f7732e9d624c6c61548ab5fb8cd410220181522ec8eca07de4860a4acdd12909d831cc56cbbac4622082221a8768d1d0901", // sigscript
4294967295, // sequence
"410411db93e1dcdb8a016b49840f8c53bc1eb68a382e97b1482ecad7b148a6909a5cb2e0eaddfb84ccf9744464f82e160bfa9b8b64f9d4c03f999b8643f656b412a3ac", // pkscript
5000000000, // value
"12cbQLTFMXRnSzktFkuoG3eHoMeFtpTu3S", // address
[] // witness
],
]],
[[ // outputs
"1Q2TWHE3GMdB6BZKafqwxXtWAWgFt5Jvm3", // address
"4104ae1a62fe09c5f51b13905f07f06b99a2f7159b2225f374cd378d71302fa28414e7aab37397f554a7df5f142c21c1b7303b8a0626f1baded5c72a704f7e6cd84cac", // pkscript
1000000000, // value
true, // spent
[ // spender
"ea44e97271691990157559d0bdd9959e02790c34db6c006d779e82fa5aee708e", // txid
0 // input
]
],
[
"12cbQLTFMXRnSzktFkuoG3eHoMeFtpTu3S", // address
"410411db93e1dcdb8a016b49840f8c53bc1eb68a382e97b1482ecad7b148a6909a5cb2e0eaddfb84ccf9744464f82e160bfa9b8b64f9d4c03f999b8643f656b412a3ac", // pkscript
4000000000, //value
true, // spent
[ // spender
"a16f3ce4dd5deb92d98ef5cf8afeaf0775ebca408f708b2146c4fb42b41e14be", // txid
0 // input
]
]]
];Accessing data
Given the following data structure:
blockArray = [169, [header, tx0, tx1], 171];Here is how you could access the the following values of Block 170:
The value of the second output of tx1
const tx1Val = blockArray[1][2][10][1][2];The hash of the block
const blockHash = blockArray[1][0][4];All the input values of tx0
const tx0Input = blockArray[1][1][9];Additional Considerations
The organisation of the data, proposed above, is simply an example of how this information could be structured. In this example blockArray is a 6-dimensional array however the data could also be organized into a dict. This structure will depend on the intrinsic and visual intentions of the project. To see how the data for the 'genesis' collection will be structured please see the genesis page.
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