I've created a LED lamp controlled by an Arduino Uno, you can modify the code to change the light pattern. I've added a pattern that imitates a fire. You can search for tutorials online for using an arduinop with a neo pixel ring, it's pretty simple and you can find different light patterns.

Hope you enjoy!

ARDUINO CODE:

/**

• Arduino Uno - NeoPixel Fire
• v. 1.0
• Copyright (C) 2015 Robert Ulbricht
• This program is free software: you can redistribute it and/or modify
• it under the terms of the GNU General Public License as published by
• the Free Software Foundation, either version 3 of the License, or
• (at your option) any later version.
• This program is distributed in the hope that it will be useful,
• but WITHOUT ANY WARRANTY; without even the implied warranty of
• MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
• GNU General Public License for more details.
• You should have received a copy of the GNU General Public License
• along with this program. If not, see .
  */

include

// data pin

define PIN 2

// led count

define CNT 24

// Parameter 1 = number of pixels in strip
// Parameter 2 = pin number (most are valid)
// Parameter 3 = pixel type flags, add together as needed:
// NEO_RGB Pixels are wired for RGB bitstream
// NEO_GRB Pixels are wired for GRB bitstream
// NEO_KHZ400 400 KHz bitstream (e.g. FLORA pixels)
// NEO_KHZ800 800 KHz bitstream (e.g. High Density LED strip)
Adafruit_NeoPixel strip = Adafruit_NeoPixel(CNT, PIN, NEO_GRB + NEO_KHZ800);

uint32_t fire_color = strip.Color ( 80, 35, 00);
uint32_t off_color = strip.Color ( 0, 0, 0);

///
/// Fire simulator
///
class NeoFire
{
Adafruit_NeoPixel &strip;
public:

NeoFire(Adafruit_NeoPixel&);
void Draw();
void Clear();
void AddColor(uint8_t position, uint32_t color);
void SubstractColor(uint8_t position, uint32_t color);
uint32_t Blend(uint32_t color1, uint32_t color2);
uint32_t Substract(uint32_t color1, uint32_t color2);
};

///
/// Constructor
///
NeoFire::NeoFire(Adafruit_NeoPixel& n_strip)
: strip (n_strip)
{
}

///
/// Set all colors
///
void NeoFire::Draw()
{
Clear();

for(int i=0;i {
AddColor(i, fire_color);
int r = random(80);
uint32_t diff_color = strip.Color ( r, r/2, r/2);
SubstractColor(i, diff_color);
}

strip.show();
}

///
/// Set color of LED
///
void NeoFire::AddColor(uint8_t position, uint32_t color)
{
uint32_t blended_color = Blend(strip.getPixelColor(position), color);
strip.setPixelColor(position, blended_color);
}

///
/// Set color of LED
///
void NeoFire::SubstractColor(uint8_t position, uint32_t color)
{
uint32_t blended_color = Substract(strip.getPixelColor(position), color);
strip.setPixelColor(position, blended_color);
}

///
/// Color blending
///
uint32_t NeoFire::Blend(uint32_t color1, uint32_t color2)
{
uint8_t r1,g1,b1;
uint8_t r2,g2,b2;
uint8_t r3,g3,b3;

r1 = (uint8_t)(color1 >> 16),
g1 = (uint8_t)(color1 >> 8),
b1 = (uint8_t)(color1 >> 0);

r2 = (uint8_t)(color2 >> 16),
g2 = (uint8_t)(color2 >> 8),
b2 = (uint8_t)(color2 >> 0);

return strip.Color(constrain(r1+r2, 0, 255), constrain(g1+g2, 0, 255), constrain(b1+b2, 0, 255));
}

///
/// Color blending
///
uint32_t NeoFire::Substract(uint32_t color1, uint32_t color2)
{
uint8_t r1,g1,b1;
uint8_t r2,g2,b2;
uint8_t r3,g3,b3;
int16_t r,g,b;

r1 = (uint8_t)(color1 >> 16),
g1 = (uint8_t)(color1 >> 8),
b1 = (uint8_t)(color1 >> 0);

r2 = (uint8_t)(color2 >> 16),
g2 = (uint8_t)(color2 >> 8),
b2 = (uint8_t)(color2 >> 0);

r=(int16_t)r1-(int16_t)r2;
g=(int16_t)g1-(int16_t)g2;
b=(int16_t)b1-(int16_t)b2;
if(r<0) r=0;
if(g<0) g=0;
if(b<0) b=0;

return strip.Color(r, g, b);
}

///
/// Every LED to black
///
void NeoFire::Clear()
{
for(uint16_t i=0; i strip.setPixelColor(i, off_color);
}

NeoFire fire(strip);

///
/// Setup
///
void setup()
{
strip.begin();
strip.show(); // Initialize all pixels to 'off'
}

///
/// Main loop
///
void loop()
{
fire.Draw();
delay(random(50,150));
}