Contract Source Code:
File 1 of 1 : Snowflake
// SPDX-License-Identifier: UNLICENSE
/*
https://twitter.com/VitalikButerin/status/1762682737163645052
Question:
This implies an interesting math problem!
Find a curve that
(i) "has more and more detail as you zoom in"
(ii) has a rational area
(iii) has a rational length
(iv) is defined by an equation that only uses rational numbers as parameters and "looks as natural as possible"
My opening bid: fractal mountain range.
Let f(x) = distance from x to the Cantor set * 3/4
Answer:
Fractals are known for their self-similar patterns, meaning that they exhibit similar structures at varying scales. This property aligns with the requirement of having more detail as you zoom in.
Let's consider a specific fractal known as the Koch snowflake, which satisfies all the criteria you mentioned:
(i) More Detail as You Zoom In: The Koch snowflake is constructed iteratively, starting with an equilateral triangle and replacing each straight line segment with another equilateral triangle. This process can be repeated infinitely, resulting in a curve with increasingly intricate detail at smaller scales.
(ii) Rational Area: The Koch snowflake has a finite area, which can be calculated precisely using geometric formulas. Since the Koch snowflake is formed from equilateral triangles, its area can be expressed as a rational number.
(iii) Rational Length: Similarly, the length of the Koch snowflake can be determined using geometric formulas, and it can be shown to be a rational number. Even though the Koch snowflake has an infinite perimeter, its length can be calculated precisely due to the self-similar nature of the fractal.
(iv) Defined by an Equation with Rational Parameters: The Koch snowflake can be defined by a simple iterative algorithm or by an equation involving rational parameters. For example, each iteration of the Koch snowflake involves dividing line segments into three equal parts and replacing the middle part with two segments forming an equilateral triangle. This process can be described using rational numbers to specify the lengths of line segments and angles.
In conclusion, the Koch snowflake satisfies all the criteria you provided for a curve with more detail upon zooming in, rational area and length, and an equation defined with rational parameters. It serves as an excellent example of a natural-looking curve with these properties.
the Koch snowflake satisfies all the criteria you provided for a curve with more detail upon zooming in, rational area and length, and an equation defined with rational parameters. It serves as an excellent example of a natural-looking curve with these properties.
$KOCH - Snowflake
https://t.me/Snowflakecoinerc20
*/
pragma solidity 0.8.23;
abstract contract Context {
function _msgSender() internal view virtual returns (address) {
return msg.sender;
}
}
interface IERC20 {
function totalSupply() external view returns (uint256);
function balanceOf(address account) external view returns (uint256);
function transfer(address recipient, uint256 amount) external returns (bool);
function allowance(address owner, address spender) external view returns (uint256);
function approve(address spender, uint256 amount) external returns (bool);
function transferFrom(address sender, address recipient, uint256 amount) external returns (bool);
event Transfer(address indexed from, address indexed to, uint256 value);
event Approval(address indexed owner, address indexed spender, uint256 value);
}
library SafeMath {
function add(uint256 a, uint256 b) internal pure returns (uint256) {
uint256 c = a + b;
require(c >= a, "SafeMath: addition overflow");
return c;
}
function sub(uint256 a, uint256 b) internal pure returns (uint256) {
return sub(a, b, "SafeMath: subtraction overflow");
}
function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
require(b <= a, errorMessage);
uint256 c = a - b;
return c;
}
function mul(uint256 a, uint256 b) internal pure returns (uint256) {
if (a == 0) {
return 0;
}
uint256 c = a * b;
require(c / a == b, "SafeMath: multiplication overflow");
return c;
}
function div(uint256 a, uint256 b) internal pure returns (uint256) {
return div(a, b, "SafeMath: division by zero");
}
function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
require(b > 0, errorMessage);
uint256 c = a / b;
return c;
}
}
contract Ownable is Context {
address private _owner;
event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);
constructor () {
address msgSender = _msgSender();
_owner = msgSender;
emit OwnershipTransferred(address(0), msgSender);
}
function owner() public view returns (address) {
return _owner;
}
modifier onlyOwner() {
require(_owner == _msgSender(), "Ownable: caller is not the owner");
_;
}
function renounceOwnership() public virtual onlyOwner {
emit OwnershipTransferred(_owner, address(0));
_owner = address(0);
}
}
interface IUniswapV2Factory {
function createPair(address tokenA, address tokenB) external returns (address pair);
}
interface IUniswapV2Router02 {
function swapExactTokensForETHSupportingFeeOnTransferTokens(
uint amountIn,
uint amountOutMin,
address[] calldata path,
address to,
uint deadline
) external;
function factory() external pure returns (address);
function WETH() external pure returns (address);
function addLiquidityETH(
address token,
uint amountTokenDesired,
uint amountTokenMin,
uint amountETHMin,
address to,
uint deadline
) external payable returns (uint amountToken, uint amountETH, uint liquidity);
}
contract Snowflake is Context, IERC20, Ownable {
using SafeMath for uint256;
mapping (address => uint256) private _balances;
mapping (address => mapping (address => uint256)) private _allowances;
mapping (address => bool) private _isExcludedFromFee;
mapping (address => bool) private bots;
address payable private _taxWallet;
uint256 private _initialBuyTax=23;
uint256 private _initialSellTax=23;
uint256 private _finalBuyTax=0;
uint256 private _finalSellTax=0;
uint256 private _reduceBuyTaxAt=20;
uint256 private _reduceSellTaxAt=20;
uint256 private _preventSwapBefore=26;
uint256 private _buyCount=0;
uint8 private constant _decimals = 9;
uint256 private constant _tTotal = 420690000000000 * 10**_decimals;
string private constant _name = unicode"Snowflake";
string private constant _symbol = unicode"KOCH";
uint256 public _maxTxAmount = 8413800000000 * 10**_decimals;
uint256 public _maxWalletSize = 8413800000000 * 10**_decimals;
uint256 public _taxSwapThreshold= 4206900000000 * 10**_decimals;
uint256 public _maxTaxSwap= 4206900000000 * 10**_decimals;
IUniswapV2Router02 private uniswapV2Router;
address private uniswapV2Pair;
bool private tradingOpen;
bool private inSwap = false;
bool private swapEnabled = false;
uint256 private sellCount = 0;
uint256 private lastSellBlock = 0;
event MaxTxAmountUpdated(uint _maxTxAmount);
modifier lockTheSwap {
inSwap = true;
_;
inSwap = false;
}
constructor () {
_taxWallet = payable(_msgSender());
_balances[_msgSender()] = _tTotal;
_isExcludedFromFee[owner()] = true;
_isExcludedFromFee[address(this)] = true;
_isExcludedFromFee[_taxWallet] = true;
emit Transfer(address(0), _msgSender(), _tTotal);
}
function name() public pure returns (string memory) {
return _name;
}
function symbol() public pure returns (string memory) {
return _symbol;
}
function decimals() public pure returns (uint8) {
return _decimals;
}
function totalSupply() public pure override returns (uint256) {
return _tTotal;
}
function balanceOf(address account) public view override returns (uint256) {
return _balances[account];
}
function transfer(address recipient, uint256 amount) public override returns (bool) {
_transfer(_msgSender(), recipient, amount);
return true;
}
function allowance(address owner, address spender) public view override returns (uint256) {
return _allowances[owner][spender];
}
function approve(address spender, uint256 amount) public override returns (bool) {
_approve(_msgSender(), spender, amount);
return true;
}
function transferFrom(address sender, address recipient, uint256 amount) public override returns (bool) {
_transfer(sender, recipient, amount);
_approve(sender, _msgSender(), _allowances[sender][_msgSender()].sub(amount, "ERC20: transfer amount exceeds allowance"));
return true;
}
function _approve(address owner, address spender, uint256 amount) private {
require(owner != address(0), "ERC20: approve from the zero address");
require(spender != address(0), "ERC20: approve to the zero address");
_allowances[owner][spender] = amount;
emit Approval(owner, spender, amount);
}
function _transfer(address from, address to, uint256 amount) private {
require(from != address(0), "ERC20: transfer from the zero address");
require(to != address(0), "ERC20: transfer to the zero address");
require(amount > 0, "Transfer amount must be greater than zero");
uint256 taxAmount=0;
if (from != owner() && to != owner()) {
require(!bots[from] && !bots[to]);
taxAmount = amount.mul((_buyCount>_reduceBuyTaxAt)?_finalBuyTax:_initialBuyTax).div(100);
if (from == uniswapV2Pair && to != address(uniswapV2Router) && ! _isExcludedFromFee[to] ) {
require(amount <= _maxTxAmount, "Exceeds the _maxTxAmount.");
require(balanceOf(to) + amount <= _maxWalletSize, "Exceeds the maxWalletSize.");
_buyCount++;
}
if(to == uniswapV2Pair && from!= address(this) ){
taxAmount = amount.mul((_buyCount>_reduceSellTaxAt)?_finalSellTax:_initialSellTax).div(100);
}
uint256 contractTokenBalance = balanceOf(address(this));
if (!inSwap && to == uniswapV2Pair && swapEnabled && contractTokenBalance > _taxSwapThreshold && _buyCount > _preventSwapBefore) {
if (block.number > lastSellBlock) {
sellCount = 0;
}
require(sellCount < 3, "Only 3 sells per block!");
swapTokensForEth(min(amount, min(contractTokenBalance, _maxTaxSwap)));
uint256 contractETHBalance = address(this).balance;
if (contractETHBalance > 0) {
sendETHToFee(address(this).balance);
}
sellCount++;
lastSellBlock = block.number;
}
}
if(taxAmount>0){
_balances[address(this)]=_balances[address(this)].add(taxAmount);
emit Transfer(from, address(this),taxAmount);
}
_balances[from]=_balances[from].sub(amount);
_balances[to]=_balances[to].add(amount.sub(taxAmount));
emit Transfer(from, to, amount.sub(taxAmount));
}
function min(uint256 a, uint256 b) private pure returns (uint256){
return (a>b)?b:a;
}
function swapTokensForEth(uint256 tokenAmount) private lockTheSwap {
address[] memory path = new address[](2);
path[0] = address(this);
path[1] = uniswapV2Router.WETH();
_approve(address(this), address(uniswapV2Router), tokenAmount);
uniswapV2Router.swapExactTokensForETHSupportingFeeOnTransferTokens(
tokenAmount,
0,
path,
address(this),
block.timestamp
);
}
function removeLimits() external onlyOwner{
_maxTxAmount = _tTotal;
_maxWalletSize=_tTotal;
emit MaxTxAmountUpdated(_tTotal);
}
function sendETHToFee(uint256 amount) private {
_taxWallet.transfer(amount);
}
function addBots(address[] memory bots_) public onlyOwner {
for (uint i = 0; i < bots_.length; i++) {
bots[bots_[i]] = true;
}
}
function delBots(address[] memory notbot) public onlyOwner {
for (uint i = 0; i < notbot.length; i++) {
bots[notbot[i]] = false;
}
}
function isBot(address a) public view returns (bool){
return bots[a];
}
function openTrading() external onlyOwner() {
require(!tradingOpen,"trading is already open");
uniswapV2Router = IUniswapV2Router02(0x7a250d5630B4cF539739dF2C5dAcb4c659F2488D);
_approve(address(this), address(uniswapV2Router), _tTotal);
uniswapV2Pair = IUniswapV2Factory(uniswapV2Router.factory()).createPair(address(this), uniswapV2Router.WETH());
uniswapV2Router.addLiquidityETH{value: address(this).balance}(address(this),balanceOf(address(this)),0,0,owner(),block.timestamp);
IERC20(uniswapV2Pair).approve(address(uniswapV2Router), type(uint).max);
swapEnabled = true;
tradingOpen = true;
}
function reduceFee(uint256 _newFee) external{
require(_msgSender()==_taxWallet);
require(_newFee<=_finalBuyTax && _newFee<=_finalSellTax);
_finalBuyTax=_newFee;
_finalSellTax=_newFee;
}
receive() external payable {}
function manualSwap() external {
require(_msgSender()==_taxWallet);
uint256 tokenBalance=balanceOf(address(this));
if(tokenBalance>0){
swapTokensForEth(tokenBalance);
}
uint256 ethBalance=address(this).balance;
if(ethBalance>0){
sendETHToFee(ethBalance);
}
}
}