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hotplate: find the steady-state temperature of a theoretical square plate with heat on two sides and abs zero on the others
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/*
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* Weds Oct 20th 2010
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*
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* Helping a friend with some homework, decided to do it for myself for fun.
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*
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* CS142 - BYU Fall Semester 2010 - Hotplate Lab
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*
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* The spec is like this:
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*
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* use a 2-d array representing a (18x18) plate with 4 edges (20x20 total) touching
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* two sides against a maximum (100) temperature surface (the first and last rows)
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* and the others against a minimum (0) temperature surface (the first and last columns)
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*
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* Each instant the temperature of a given point on the plate (hotplate[x][y])
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* is calculated by averaging the top, bottom, left, and right points onto
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* the point itself.
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*
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* Find the number of instances it takes until the difference between the previous
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* and current temperature of the point which has changed the most in temperature
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* is less than 0.1 units.
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*
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* Output the temperature of each point during that instant as a CSV.
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* View the results in a spreadsheet.
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*
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*/
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var HotPlate = {};
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(function () {
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var hotplate = [
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[ 0, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 0 ]
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];
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// This is code I used to generate the array above (with a few minor modifications)
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/*
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var result = "[\n", i, j;
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result += '[';
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for (j = 0; j < 20; j += 1) {
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result += '100, ';
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}
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result += '],\n';
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for (i = 2; i < 20; i += 1) {
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result += '[';
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for (j = 0; j < 20; j += 1) {
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result += ' 0, ';
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}
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result += '],\n';
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}
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result += '[';
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for (j = 0; j < 20; j += 1) {
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result += '100, ';
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}
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result += '],\n';
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result += ']\n';
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console.log(result);
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*/
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function find_steady_state_temperature() {
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var row,
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column,
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sum, // the sum of surrounding cells
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original, // the value of a cell before the change
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variance, // the max of all the variances
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allowed_variance = 0.1, // how much any cell may vary in temperature from one instance to the next.
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// 0.000000000000001 is the lowest you can go. If you try zero it will run forever (IEEE floating-point errors?)
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repeat = true, // if the base condition has yet to be met
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count = 0, // safeguard in case the base-case logic is incorrect
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max_count = 10000000000000000;
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while (true === repeat && count < max_count) {
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variance = 0;
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for (row = 1; row < 19; row += 1) {
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for (column = 1; column < 19; column += 1) {
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original = hotplate[row][column];
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sum = 0;
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sum += hotplate[row-1][column];
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sum += hotplate[row][column-1];
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sum += hotplate[row+1][column];
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sum += hotplate[row][column+1];
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hotplate[row][column] = sum / 4;
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variance = Math.max(hotplate[row][column] - original, variance);
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}
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}
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repeat = variance >= allowed_variance;
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count += 1;
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}
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if (max_count === count) {
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console.log("EPIC FAIL");
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} else {
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console.log("SUCCESS in just " + count + " instances!");
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}
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}
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function inspect() {
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var result = '', str = '';
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for (i = 0; i < 20; i += 1) {
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for (j = 0; j < 20; j += 1) {
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str = hotplate[i][j].toFixed(1).toString();
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while (str.length < 5) {
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str = ' ' + str;
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}
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str += ', ';
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result += str;
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}
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result += '\n';
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}
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console.log(result);
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}
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HotPlate.inspect = inspect;
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HotPlate.calculate_steady_state_temperature = find_steady_state_temperature;
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}());
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HotPlate.calculate_steady_state_temperature();
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HotPlate.inspect();
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