The present work adapts the lambda cold dark matter ΛCDM model for simulating 106 dark matter and 106 gas particles to form galaxies inside a box of size (70Mpc/h)3. The simulation is shown from high redshift z=10(1.2Gyr.) after the Big Bang to the low redshift z=0(13.4Gyr.) which represents the present day. The position of the particles and the temperature-density relations were studied at each epoch. It is found that the galaxies formation start at low redshift z=5 and the gas cooled at 104 K. The web construction of voids, filaments and clusters of galaxies were observed clearly at z=0. Sixteen processors of high performance supercomputer of Nottingham University-England were used in the simulation and the run took more than one day.