This should be enough to get you started. This plots a julia set in ascii. If you want to plot the mandelbrot set instead, iterate over c instead of z.

#include <stdio.h>

typedef struct tag_complex
{
    double real, imag;
} complex;

static complex complex_mul(
const complex* a,
const complex* b)
{
  /*   a * b = (a_real + i*a_imag)(b_real + i*b_imag) */
  /* i*i = -1, hence imag*imag becomes -(imag*imag) */     
  complex ret;

  ret.real = a->real*b->real - a->imag*b->imag;
  ret.imag = a->real*b->imag + a->imag*b->real;
  return ret;
}

static complex complex_add(
const complex* a,
const complex* b)
{
  complex ret;

  ret.real = a->real + b->real;
  ret.imag = a->imag + b->imag;
  return ret;
}

static int julia(
complex* z,
const complex* c,
int maxIter)
{
  double lengthSquared;
  int iter = 0;

  while(iter < maxIter){
    ++iter;
    *z = complex_mul(z, z);
    *z = complex_add(z, c);
    lengthSquared = z->real*z->real + z->imag*z->imag;
    /* If the point escapes the radius 2
       in the complex plane, it s in the set */
    if(lengthSquared > 4.0)
      return iter;
  }
  /* Point didn t escape. Either it s not in the set,
     or we need more iterations.*/
  return 0;
}

int main(int argc, char* argv[])
{
  const int width = 80;
  const int height = 40;
  const int maxIter = 512;

  /* step in the range [0, 4] since the set
     lives within [-2, 2] in the complex space */
  const double step_height = 4.0 / (double)height;
  const double step_width = 4.0 / (double)width;

  /*c is constant for julia sets. z is iterated over */
  const complex c = {0.285, 0.0};

  complex z;
  int index;
  char ch;
  for(int j=0; j<height; ++j){
    for(int i=0; i<width; ++i){
      /* Get interpolants within [-2, 2] range */
      z.imag = ((double)j * step_height) - 2.0;
      z.real = ((double)i * step_width) - 2.0;
      index = julia(&z, &c, maxIter);
      ch = (index % ( Z  -    )) +    ;
      printf("%c", ch);
    }
    printf("
");
    fflush(stdout);
  }
}